Youtor
Laurent series
YOUR LINK HERE:
http://youtube.com/watch?v=LD8kCCaxUQE
We derive the Laurent series for functions that are non analytic at a point z_0 by utilizing the same technique as Taylor series, where we use the Cauchy integral formula. Because there is a point of non-analyticity, the contours form a multiply connected domain that yields additional terms beyond that of a standard Taylor series.","styleRuns":[{"startIndex":0,"length":332,"styleRunExtensions":{"styleRunColorMapExtension":{"colorMap":[{"key":"USER_INTERFACE_THEME_DARK","value":4294967295},{"key":"USER_INTERFACE_THEME_LIGHT","value":4279440147}]}},"fontFamilyName":"Roboto"}]},"headerRuns":[{"startIndex":0,"length":332,"headerMapping":"ATTRIBUTED_STRING_HEADER_MAPPING_UNSPECIFIED"}]}},{"compositeVideoPrimaryInfoRenderer":{}},{"itemSectionRenderer":{"contents":[{"continuationItemRenderer":{"trigger":"CONTINUATION_TRIGGER_ON_ITEM_SHOWN","continuationEndpoint":{"clickTrackingParams":"CLYBELsvGAMiEwitgKX_27mMAxVxRnoFHUkrKso=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/next"}},"continuationCommand":{"token":"Eg0SC0xEOGtDQ2F4VVFFGAYyJSIRIgtMRDhrQ0NheFVRRTAAeAJCEGNvbW1lbnRzLXNlY3Rpb24%3D","request":"CONTINUATION_REQUEST_TYPE_WATCH_NEXT"}}}}],"trackingParams":"CLYBELsvGAMiEwitgKX_27mMAxVxRnoFHUkrKso=","sectionIdentifier":"comment-item-section","targetId":"comments-section"}}],"trackingParams":"CLUBELovIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},"secondaryResults":{"secondaryResults":{"results":[{"compactVideoRenderer":{"videoId":"jcIzGkZlpYg","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/jcIzGkZlpYg/hqdefault.jpg?sqp=-oaymwE1CKgBEF5IVfKriqkDKAgBFQAAiEIYAXABwAEG8AEB-AH-CYAC0AWKAgwIABABGGUgZShlMA8= rs=AOn4CLAd-vCsQnX_llh4mT2fUpkcsK1U6w","width":168,"height":94},{"url":"https://i.ytimg.com/vi/jcIzGkZlpYg/hqdefault.jpg?sqp=-oaymwE2CNACELwBSFXyq4qpAygIARUAAIhCGAFwAcABBvABAfgB_gmAAtAFigIMCAAQARhlIGUoZTAP rs=AOn4CLBmqg3n-gH0g9y-WTQaFye5rwpgag","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Examples of Laurent series computations ΠΎΡ „William Nesse“ 27 646 ΠΏΠΎΠΊΠ°Π·Π²Π°Π½ΠΈΡ ΠΏΡΠ΅Π΄ΠΈ 10 Π³ΠΎΠ΄ΠΈΠ½ΠΈ 27 ΠΌΠΈΠ½ΡΡΠΈ"}},"simpleText":"Examples of Laurent series computations"},"longBylineText":{"runs":[{"text":"William Nesse","navigationEndpoint":{"clickTrackingParams":"CK4BEKQwGAAiEwitgKX_27mMAxVxRnoFHUkrKsoyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@WilliamNesse","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCXv696SjJra5Ih3sZB0bb1g","canonicalBaseUrl":"/@WilliamNesse"}}}]},"publishedTimeText":{"simpleText":"ΠΏΡΠ΅Π΄ΠΈ 10 Π³ΠΎΠ΄ΠΈΠ½ΠΈ"},"viewCountText":{"simpleText":"27 646 ΠΏΠΎΠΊΠ°Π·Π²Π°Π½ΠΈΡ"},"lengthText":{"accessibility":{"accessibilityData":{"label":"27 ΠΌΠΈΠ½ΡΡΠΈ ΠΈ 22 ΡΠ΅ΠΊΡΠ½Π΄ΠΈ"}},"simpleText":"27:22"},"navigationEndpoint":{"clickTrackingParams":"CK4BEKQwGAAiEwitgKX_27mMAxVxRnoFHUkrKsoyB3JlbGF0ZWRIgaLFtYKByZ8smgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=jcIzGkZlpYg","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"jcIzGkZlpYg","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 onvi=1 id=8dc2331a4665a588 ip=185.82.219.199 initcwndbps=1335000 mt=1743609206 oweuc= pxtags=Cg4KAnR4Egg1MTQxNDI0MA rxtags=Cg4KAnR4Egg1MTQxNDIzOQ%2CCg4KAnR4Egg1MTQxNDI0MA"}}}}},"shortBylineText":{"runs":[{"text":"William Nesse","navigationEndpoint":{"clickTrackingParams":"CK4BEKQwGAAiEwitgKX_27mMAxVxRnoFHUkrKsoyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@WilliamNesse","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCXv696SjJra5Ih3sZB0bb1g","canonicalBaseUrl":"/@WilliamNesse"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_kdUmgd8KarbFQSv12leEHw3yJQ12KeYrMheuiHVZO8XXM=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CK4BEKQwGAAiEwitgKX_27mMAxVxRnoFHUkrKspAiMuWs6TjjOGNAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"27 Ρ ΠΈΠ»ΡΠ΄ΠΈ ΠΏΠΎΠΊΠ°Π·Π²Π°Π½ΠΈΡ"}},"simpleText":"27 Ρ ΠΈΠ». ΠΏΠΎΠΊΠ°Π·Π²Π°Π½ΠΈΡ"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"ΠΠΎΠ±Π°Π²ΡΠ½Π΅ Π² ΠΎΠΏΠ°ΡΠΊΠ°ΡΠ°"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CLMBEP6YBBgFIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLMBEP6YBBgFIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"jcIzGkZlpYg","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLMBEP6YBBgFIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["jcIzGkZlpYg"],"params":"CAQ%3D"}},"videoIds":["jcIzGkZlpYg"]}},{"clickTrackingParams":"CLMBEP6YBBgFIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"ΠΠΎΠ±Π°Π²Π΅Π½ Π² ΠΎΠΏΠ°ΡΠΊΠ°ΡΠ°"},"trackingParams":"CLQBELlqIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},"popupType":"TOAST"}}]}},"trackingParams":"CLMBEP6YBBgFIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CLIBENGqBRgGIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","offlineVideoEndpoint":{"videoId":"jcIzGkZlpYg","onAddCommand":{"clickTrackingParams":"CLIBENGqBRgGIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","getDownloadActionCommand":{"videoId":"jcIzGkZlpYg","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CLIBENGqBRgGIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Π‘ΠΏΠΎΠ΄Π΅Π»ΡΠ½Π΅"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CK4BEKQwGAAiEwitgKX_27mMAxVxRnoFHUkrKso=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtqY0l6R2tabHBZZw%3D%3D","commands":[{"clickTrackingParams":"CK4BEKQwGAAiEwitgKX_27mMAxVxRnoFHUkrKso=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CLEBEI5iIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CK4BEKQwGAAiEwitgKX_27mMAxVxRnoFHUkrKso=","hasSeparator":true}}],"trackingParams":"CK4BEKQwGAAiEwitgKX_27mMAxVxRnoFHUkrKso=","accessibility":{"accessibilityData":{"label":"ΠΠ΅Π½Ρ Π·Π° Π΄Π΅ΠΉΡΡΠ²ΠΈΡ"}},"targetId":"watch-related-menu-button"}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"27 ΠΌΠΈΠ½ΡΡΠΈ ΠΈ 22 ΡΠ΅ΠΊΡΠ½Π΄ΠΈ"}},"simpleText":"27:22"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"ΠΠ° Π³Π»Π΅Π΄Π°Π½Π΅ ΠΏΠΎ-ΠΊΡΡΠ½ΠΎ","toggledTooltip":"ΠΠΎΠ±Π°Π²Π΅Π½","untoggledServiceEndpoint":{"clickTrackingParams":"CLABEPnnAxgBIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"jcIzGkZlpYg","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CLABEPnnAxgBIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"jcIzGkZlpYg"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"ΠΠ° Π³Π»Π΅Π΄Π°Π½Π΅ ΠΏΠΎ-ΠΊΡΡΠ½ΠΎ"}},"toggledAccessibility":{"accessibilityData":{"label":"ΠΠΎΠ±Π°Π²Π΅Π½"}},"trackingParams":"CLABEPnnAxgBIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"ΠΠΎΠ±Π°Π²ΡΠ½Π΅ Π² ΠΎΠΏΠ°ΡΠΊΠ°ΡΠ°","toggledTooltip":"ΠΠΎΠ±Π°Π²Π΅Π½","untoggledServiceEndpoint":{"clickTrackingParams":"CK8BEMfsBBgCIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CK8BEMfsBBgCIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"jcIzGkZlpYg","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CK8BEMfsBBgCIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["jcIzGkZlpYg"],"params":"CAQ%3D"}},"videoIds":["jcIzGkZlpYg"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"ΠΠΎΠ±Π°Π²ΡΠ½Π΅ Π² ΠΎΠΏΠ°ΡΠΊΠ°ΡΠ°"}},"toggledAccessibility":{"accessibilityData":{"label":"ΠΠΎΠ±Π°Π²Π΅Π½"}},"trackingParams":"CK8BEMfsBBgCIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Π‘Π΅Π³Π° ΡΠ»ΡΡΠ°ΡΠ΅"}]}}}],"accessibility":{"accessibilityData":{"label":"Examples of Laurent series computations – 27 ΠΌΠΈΠ½ΡΡΠΈ – ΠΡΠΌ ΠΊΠ°Π½Π°Π»Π° – William Nesse - 27 Ρ ΠΈΠ». ΠΏΠΎΠΊΠ°Π·Π²Π°Π½ΠΈΡ - ΠΏΡΠ΅Π΄ΠΈ 10 Π³ΠΎΠ΄ΠΈΠ½ΠΈ – ΠΏΡΡΠΊΠ°Π½Π΅ Π½Π° Π²ΠΈΠ΄Π΅ΠΎΠΊΠ»ΠΈΠΏΠ°"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"cuuKTy29UMA","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/cuuKTy29UMA/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLBAVJxF22BDhCGiGetX3jp33_Cpiw","width":168,"height":94},{"url":"https://i.ytimg.com/vi/cuuKTy29UMA/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLBsu9-ApqfVw5Q9D8-XXKlq_VPhhA","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Laurent's Theorem - Complex Analysis by a Physicist ΠΎΡ „Nick Space Cowboy“ 19 176 ΠΏΠΎΠΊΠ°Π·Π²Π°Π½ΠΈΡ ΠΏΡΠ΅Π΄ΠΈ 3 Π³ΠΎΠ΄ΠΈΠ½ΠΈ 9 ΠΌΠΈΠ½ΡΡΠΈ ΠΈ 55 ΡΠ΅ΠΊΡΠ½Π΄ΠΈ"}},"simpleText":"Laurent's Theorem - Complex Analysis by a Physicist"},"longBylineText":{"runs":[{"text":"Nick Space Cowboy","navigationEndpoint":{"clickTrackingParams":"CKcBEKQwGAEiEwitgKX_27mMAxVxRnoFHUkrKsoyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@nspace-cowboy","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCYL6H7DokSvUMzEJGvLI3RQ","canonicalBaseUrl":"/@nspace-cowboy"}}}]},"publishedTimeText":{"simpleText":"ΠΏΡΠ΅Π΄ΠΈ 3 Π³ΠΎΠ΄ΠΈΠ½ΠΈ"},"viewCountText":{"simpleText":"19 176 ΠΏΠΎΠΊΠ°Π·Π²Π°Π½ΠΈΡ"},"lengthText":{"accessibility":{"accessibilityData":{"label":"9 ΠΌΠΈΠ½ΡΡΠΈ ΠΈ 55 ΡΠ΅ΠΊΡΠ½Π΄ΠΈ"}},"simpleText":"9:55"},"navigationEndpoint":{"clickTrackingParams":"CKcBEKQwGAEiEwitgKX_27mMAxVxRnoFHUkrKsoyB3JlbGF0ZWRIgaLFtYKByZ8smgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=cuuKTy29UMA","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"cuuKTy29UMA","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 onvi=1 id=72eb8a4f2dbd50c0 ip=185.82.219.199 initcwndbps=1335000 mt=1743609206 oweuc= pxtags=Cg4KAnR4Egg1MTQxNDI0MA rxtags=Cg4KAnR4Egg1MTQxNDIzOQ%2CCg4KAnR4Egg1MTQxNDI0MA"}}}}},"shortBylineText":{"runs":[{"text":"Nick Space Cowboy","navigationEndpoint":{"clickTrackingParams":"CKcBEKQwGAEiEwitgKX_27mMAxVxRnoFHUkrKsoyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@nspace-cowboy","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCYL6H7DokSvUMzEJGvLI3RQ","canonicalBaseUrl":"/@nspace-cowboy"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/FGsiubej3Wh39ZI1Eqn7DR9kFcRudP8hQvbTXpsU4R8GTE3aRPNBTJSCSBUVz9bxFdIi8Z1yklI=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CKcBEKQwGAEiEwitgKX_27mMAxVxRnoFHUkrKspAwKH17fLJ4vVy","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"19 Ρ ΠΈΠ»ΡΠ΄ΠΈ ΠΏΠΎΠΊΠ°Π·Π²Π°Π½ΠΈΡ"}},"simpleText":"19 Ρ ΠΈΠ». ΠΏΠΎΠΊΠ°Π·Π²Π°Π½ΠΈΡ"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"ΠΠΎΠ±Π°Π²ΡΠ½Π΅ Π² ΠΎΠΏΠ°ΡΠΊΠ°ΡΠ°"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CKwBEP6YBBgFIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CKwBEP6YBBgFIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"cuuKTy29UMA","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CKwBEP6YBBgFIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["cuuKTy29UMA"],"params":"CAQ%3D"}},"videoIds":["cuuKTy29UMA"]}},{"clickTrackingParams":"CKwBEP6YBBgFIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"ΠΠΎΠ±Π°Π²Π΅Π½ Π² ΠΎΠΏΠ°ΡΠΊΠ°ΡΠ°"},"trackingParams":"CK0BELlqIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},"popupType":"TOAST"}}]}},"trackingParams":"CKwBEP6YBBgFIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CKsBENGqBRgGIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","offlineVideoEndpoint":{"videoId":"cuuKTy29UMA","onAddCommand":{"clickTrackingParams":"CKsBENGqBRgGIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","getDownloadActionCommand":{"videoId":"cuuKTy29UMA","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CKsBENGqBRgGIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Π‘ΠΏΠΎΠ΄Π΅Π»ΡΠ½Π΅"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CKcBEKQwGAEiEwitgKX_27mMAxVxRnoFHUkrKso=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtjdXVLVHkyOVVNQQ%3D%3D","commands":[{"clickTrackingParams":"CKcBEKQwGAEiEwitgKX_27mMAxVxRnoFHUkrKso=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CKoBEI5iIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CKcBEKQwGAEiEwitgKX_27mMAxVxRnoFHUkrKso=","hasSeparator":true}}],"trackingParams":"CKcBEKQwGAEiEwitgKX_27mMAxVxRnoFHUkrKso=","accessibility":{"accessibilityData":{"label":"ΠΠ΅Π½Ρ Π·Π° Π΄Π΅ΠΉΡΡΠ²ΠΈΡ"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"9 ΠΌΠΈΠ½ΡΡΠΈ ΠΈ 55 ΡΠ΅ΠΊΡΠ½Π΄ΠΈ"}},"simpleText":"9:55"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"ΠΠ° Π³Π»Π΅Π΄Π°Π½Π΅ ΠΏΠΎ-ΠΊΡΡΠ½ΠΎ","toggledTooltip":"ΠΠΎΠ±Π°Π²Π΅Π½","untoggledServiceEndpoint":{"clickTrackingParams":"CKkBEPnnAxgBIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"cuuKTy29UMA","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CKkBEPnnAxgBIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"cuuKTy29UMA"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"ΠΠ° Π³Π»Π΅Π΄Π°Π½Π΅ ΠΏΠΎ-ΠΊΡΡΠ½ΠΎ"}},"toggledAccessibility":{"accessibilityData":{"label":"ΠΠΎΠ±Π°Π²Π΅Π½"}},"trackingParams":"CKkBEPnnAxgBIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"ΠΠΎΠ±Π°Π²ΡΠ½Π΅ Π² ΠΎΠΏΠ°ΡΠΊΠ°ΡΠ°","toggledTooltip":"ΠΠΎΠ±Π°Π²Π΅Π½","untoggledServiceEndpoint":{"clickTrackingParams":"CKgBEMfsBBgCIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CKgBEMfsBBgCIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"cuuKTy29UMA","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CKgBEMfsBBgCIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["cuuKTy29UMA"],"params":"CAQ%3D"}},"videoIds":["cuuKTy29UMA"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"ΠΠΎΠ±Π°Π²ΡΠ½Π΅ Π² ΠΎΠΏΠ°ΡΠΊΠ°ΡΠ°"}},"toggledAccessibility":{"accessibilityData":{"label":"ΠΠΎΠ±Π°Π²Π΅Π½"}},"trackingParams":"CKgBEMfsBBgCIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Π‘Π΅Π³Π° ΡΠ»ΡΡΠ°ΡΠ΅"}]}}}],"accessibility":{"accessibilityData":{"label":"Laurent's Theorem - Complex Analysis by a Physicist – 9 ΠΌΠΈΠ½ΡΡΠΈ ΠΈ 55 ΡΠ΅ΠΊΡΠ½Π΄ΠΈ – ΠΡΠΌ ΠΊΠ°Π½Π°Π»Π° – Nick Space Cowboy - 19 Ρ ΠΈΠ». ΠΏΠΎΠΊΠ°Π·Π²Π°Π½ΠΈΡ - ΠΏΡΠ΅Π΄ΠΈ 3 Π³ΠΎΠ΄ΠΈΠ½ΠΈ – ΠΏΡΡΠΊΠ°Π½Π΅ Π½Π° Π²ΠΈΠ΄Π΅ΠΎΠΊΠ»ΠΈΠΏΠ°"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"BgweqVFEHYI","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/BgweqVFEHYI/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLCugpwrIyx5BF6O_P5Me54qWnE4ww","width":168,"height":94},{"url":"https://i.ytimg.com/vi/BgweqVFEHYI/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLBRj4mxAPRUGdP6yZK6SLVaSWAcaA","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"China | A Nice Square Root Algebra Problem | Math Olympiad ΠΎΡ „Math Hunter“ 204 ΠΏΠΎΠΊΠ°Π·Π²Π°Π½ΠΈΡ ΠΏΡΠ΅Π΄ΠΈ 1 ΡΠ°Ρ 8 ΠΌΠΈΠ½ΡΡΠΈ ΠΈ 46 ΡΠ΅ΠΊΡΠ½Π΄ΠΈ"}},"simpleText":"China | A Nice Square Root Algebra Problem | Math Olympiad"},"longBylineText":{"runs":[{"text":"Math Hunter","navigationEndpoint":{"clickTrackingParams":"CKABEKQwGAIiEwitgKX_27mMAxVxRnoFHUkrKsoyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@mathshunter","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCD8z1-fRND1pq6jX0IxS9Ow","canonicalBaseUrl":"/@mathshunter"}}}]},"publishedTimeText":{"simpleText":"ΠΏΡΠ΅Π΄ΠΈ 1 ΡΠ°Ρ"},"viewCountText":{"simpleText":"204 ΠΏΠΎΠΊΠ°Π·Π²Π°Π½ΠΈΡ"},"lengthText":{"accessibility":{"accessibilityData":{"label":"8 ΠΌΠΈΠ½ΡΡΠΈ ΠΈ 46 ΡΠ΅ΠΊΡΠ½Π΄ΠΈ"}},"simpleText":"8:46"},"navigationEndpoint":{"clickTrackingParams":"CKABEKQwGAIiEwitgKX_27mMAxVxRnoFHUkrKsoyB3JlbGF0ZWRIgaLFtYKByZ8smgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=BgweqVFEHYI","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"BgweqVFEHYI","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr1---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 onvi=1 id=060c1ea951441d82 ip=185.82.219.199 initcwndbps=1335000 mt=1743609206 oweuc= pxtags=Cg4KAnR4Egg1MTQxNDI0MA rxtags=Cg4KAnR4Egg1MTQxNDIzOQ%2CCg4KAnR4Egg1MTQxNDI0MA"}}}}},"shortBylineText":{"runs":[{"text":"Math Hunter","navigationEndpoint":{"clickTrackingParams":"CKABEKQwGAIiEwitgKX_27mMAxVxRnoFHUkrKsoyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@mathshunter","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCD8z1-fRND1pq6jX0IxS9Ow","canonicalBaseUrl":"/@mathshunter"}}}]},"badges":[{"metadataBadgeRenderer":{"style":"BADGE_STYLE_TYPE_SIMPLE","label":"ΠΠΎΠ²","trackingParams":"CKABEKQwGAIiEwitgKX_27mMAxVxRnoFHUkrKso="}}],"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/gbzA38Rb-HrBjfy0PashqUkKOt7ZB-VDYsOvitg7ZdSoC1Yabi8IT6Ili8Qnsz8ZGve9v02S7Os=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CKABEKQwGAIiEwitgKX_27mMAxVxRnoFHUkrKspAgruQipXVh4YG","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"204 ΠΏΠΎΠΊΠ°Π·Π²Π°Π½ΠΈΡ"}},"simpleText":"204 ΠΏΠΎΠΊΠ°Π·Π²Π°Π½ΠΈΡ"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"ΠΠΎΠ±Π°Π²ΡΠ½Π΅ Π² ΠΎΠΏΠ°ΡΠΊΠ°ΡΠ°"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CKUBEP6YBBgGIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CKUBEP6YBBgGIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"BgweqVFEHYI","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CKUBEP6YBBgGIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["BgweqVFEHYI"],"params":"CAQ%3D"}},"videoIds":["BgweqVFEHYI"]}},{"clickTrackingParams":"CKUBEP6YBBgGIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"ΠΠΎΠ±Π°Π²Π΅Π½ Π² ΠΎΠΏΠ°ΡΠΊΠ°ΡΠ°"},"trackingParams":"CKYBELlqIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},"popupType":"TOAST"}}]}},"trackingParams":"CKUBEP6YBBgGIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CKQBENGqBRgHIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","offlineVideoEndpoint":{"videoId":"BgweqVFEHYI","onAddCommand":{"clickTrackingParams":"CKQBENGqBRgHIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","getDownloadActionCommand":{"videoId":"BgweqVFEHYI","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CKQBENGqBRgHIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Π‘ΠΏΠΎΠ΄Π΅Π»ΡΠ½Π΅"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CKABEKQwGAIiEwitgKX_27mMAxVxRnoFHUkrKso=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtCZ3dlcVZGRUhZSQ%3D%3D","commands":[{"clickTrackingParams":"CKABEKQwGAIiEwitgKX_27mMAxVxRnoFHUkrKso=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CKMBEI5iIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CKABEKQwGAIiEwitgKX_27mMAxVxRnoFHUkrKso=","hasSeparator":true}}],"trackingParams":"CKABEKQwGAIiEwitgKX_27mMAxVxRnoFHUkrKso=","accessibility":{"accessibilityData":{"label":"ΠΠ΅Π½Ρ Π·Π° Π΄Π΅ΠΉΡΡΠ²ΠΈΡ"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"8 ΠΌΠΈΠ½ΡΡΠΈ ΠΈ 46 ΡΠ΅ΠΊΡΠ½Π΄ΠΈ"}},"simpleText":"8:46"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"ΠΠ° Π³Π»Π΅Π΄Π°Π½Π΅ ΠΏΠΎ-ΠΊΡΡΠ½ΠΎ","toggledTooltip":"ΠΠΎΠ±Π°Π²Π΅Π½","untoggledServiceEndpoint":{"clickTrackingParams":"CKIBEPnnAxgCIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"BgweqVFEHYI","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CKIBEPnnAxgCIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"BgweqVFEHYI"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"ΠΠ° Π³Π»Π΅Π΄Π°Π½Π΅ ΠΏΠΎ-ΠΊΡΡΠ½ΠΎ"}},"toggledAccessibility":{"accessibilityData":{"label":"ΠΠΎΠ±Π°Π²Π΅Π½"}},"trackingParams":"CKIBEPnnAxgCIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"ΠΠΎΠ±Π°Π²ΡΠ½Π΅ Π² ΠΎΠΏΠ°ΡΠΊΠ°ΡΠ°","toggledTooltip":"ΠΠΎΠ±Π°Π²Π΅Π½","untoggledServiceEndpoint":{"clickTrackingParams":"CKEBEMfsBBgDIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CKEBEMfsBBgDIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"BgweqVFEHYI","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CKEBEMfsBBgDIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["BgweqVFEHYI"],"params":"CAQ%3D"}},"videoIds":["BgweqVFEHYI"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"ΠΠΎΠ±Π°Π²ΡΠ½Π΅ Π² ΠΎΠΏΠ°ΡΠΊΠ°ΡΠ°"}},"toggledAccessibility":{"accessibilityData":{"label":"ΠΠΎΠ±Π°Π²Π΅Π½"}},"trackingParams":"CKEBEMfsBBgDIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Π‘Π΅Π³Π° ΡΠ»ΡΡΠ°ΡΠ΅"}]}}}],"accessibility":{"accessibilityData":{"label":"China | A Nice Square Root Algebra Problem | Math Olympiad – 8 ΠΌΠΈΠ½ΡΡΠΈ ΠΈ 46 ΡΠ΅ΠΊΡΠ½Π΄ΠΈ – ΠΡΠΌ ΠΊΠ°Π½Π°Π»Π° – Math Hunter - 204 ΠΏΠΎΠΊΠ°Π·Π²Π°Π½ΠΈΡ - ΠΏΡΠ΅Π΄ΠΈ 1 ΡΠ°Ρ – ΠΏΡΡΠΊΠ°Π½Π΅ Π½Π° Π²ΠΈΠ΄Π΅ΠΎΠΊΠ»ΠΈΠΏΠ°"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"luVIoGllnac","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/luVIoGllnac/hqdefault.jpg?sqp=-oaymwE1CKgBEF5IVfKriqkDKAgBFQAAiEIYAXABwAEG8AEB-AH-CYAC0AWKAgwIABABGGUgZShlMA8= rs=AOn4CLCAQu1l6k7uxAI7QBiBTjFmouuhzg","width":168,"height":94},{"url":"https://i.ytimg.com/vi/luVIoGllnac/hqdefault.jpg?sqp=-oaymwE2CNACELwBSFXyq4qpAygIARUAAIhCGAFwAcABBvABAfgB_gmAAtAFigIMCAAQARhlIGUoZTAP rs=AOn4CLC7W7pGl1km8Kzq0-DaguBTyEO6Fw","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Complex Analysis 11: Laurent Series ΠΎΡ „MathsStatsUNSW“ 171 573 ΠΏΠΎΠΊΠ°Π·Π²Π°Π½ΠΈΡ ΠΏΡΠ΅Π΄ΠΈ 9 Π³ΠΎΠ΄ΠΈΠ½ΠΈ 7 ΠΌΠΈΠ½ΡΡΠΈ ΠΈ 16 ΡΠ΅ΠΊΡΠ½Π΄ΠΈ"}},"simpleText":"Complex Analysis 11: Laurent Series"},"longBylineText":{"runs":[{"text":"MathsStatsUNSW","navigationEndpoint":{"clickTrackingParams":"CJkBEKQwGAMiEwitgKX_27mMAxVxRnoFHUkrKsoyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@MathsStatsUNSW","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCJgDMH0vbMaZW7T7OG5xl5A","canonicalBaseUrl":"/@MathsStatsUNSW"}}}]},"publishedTimeText":{"simpleText":"ΠΏΡΠ΅Π΄ΠΈ 9 Π³ΠΎΠ΄ΠΈΠ½ΠΈ"},"viewCountText":{"simpleText":"171 573 ΠΏΠΎΠΊΠ°Π·Π²Π°Π½ΠΈΡ"},"lengthText":{"accessibility":{"accessibilityData":{"label":"7 ΠΌΠΈΠ½ΡΡΠΈ ΠΈ 16 ΡΠ΅ΠΊΡΠ½Π΄ΠΈ"}},"simpleText":"7:16"},"navigationEndpoint":{"clickTrackingParams":"CJkBEKQwGAMiEwitgKX_27mMAxVxRnoFHUkrKsoyB3JlbGF0ZWRIgaLFtYKByZ8smgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=luVIoGllnac","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"luVIoGllnac","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr3---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 onvi=1 id=96e548a069659da7 ip=185.82.219.199 initcwndbps=1335000 mt=1743609206 oweuc= pxtags=Cg4KAnR4Egg1MTQxNDI0MA rxtags=Cg4KAnR4Egg1MTQxNDIzOQ%2CCg4KAnR4Egg1MTQxNDI0MA"}}}}},"shortBylineText":{"runs":[{"text":"MathsStatsUNSW","navigationEndpoint":{"clickTrackingParams":"CJkBEKQwGAMiEwitgKX_27mMAxVxRnoFHUkrKsoyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@MathsStatsUNSW","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCJgDMH0vbMaZW7T7OG5xl5A","canonicalBaseUrl":"/@MathsStatsUNSW"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/6sxW9hrQ1p9Dak--yZQLiri7qTqh1UyVAnhzyUPXnEqdpBFMDZY9GkBUsnLgZjhg0s_7Avgb=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CJkBEKQwGAMiEwitgKX_27mMAxVxRnoFHUkrKspAp7uWy4aU0vKWAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"171 Ρ ΠΈΠ»ΡΠ΄ΠΈ ΠΏΠΎΠΊΠ°Π·Π²Π°Π½ΠΈΡ"}},"simpleText":"171 Ρ ΠΈΠ». ΠΏΠΎΠΊΠ°Π·Π²Π°Π½ΠΈΡ"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"ΠΠΎΠ±Π°Π²ΡΠ½Π΅ Π² ΠΎΠΏΠ°ΡΠΊΠ°ΡΠ°"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CJ4BEP6YBBgGIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CJ4BEP6YBBgGIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"luVIoGllnac","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CJ4BEP6YBBgGIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["luVIoGllnac"],"params":"CAQ%3D"}},"videoIds":["luVIoGllnac"]}},{"clickTrackingParams":"CJ4BEP6YBBgGIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"ΠΠΎΠ±Π°Π²Π΅Π½ Π² ΠΎΠΏΠ°ΡΠΊΠ°ΡΠ°"},"trackingParams":"CJ8BELlqIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},"popupType":"TOAST"}}]}},"trackingParams":"CJ4BEP6YBBgGIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CJ0BENGqBRgHIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","offlineVideoEndpoint":{"videoId":"luVIoGllnac","onAddCommand":{"clickTrackingParams":"CJ0BENGqBRgHIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","getDownloadActionCommand":{"videoId":"luVIoGllnac","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CJ0BENGqBRgHIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Π‘ΠΏΠΎΠ΄Π΅Π»ΡΠ½Π΅"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CJkBEKQwGAMiEwitgKX_27mMAxVxRnoFHUkrKso=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtsdVZJb0dsbG5hYw%3D%3D","commands":[{"clickTrackingParams":"CJkBEKQwGAMiEwitgKX_27mMAxVxRnoFHUkrKso=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CJwBEI5iIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CJkBEKQwGAMiEwitgKX_27mMAxVxRnoFHUkrKso=","hasSeparator":true}}],"trackingParams":"CJkBEKQwGAMiEwitgKX_27mMAxVxRnoFHUkrKso=","accessibility":{"accessibilityData":{"label":"ΠΠ΅Π½Ρ Π·Π° Π΄Π΅ΠΉΡΡΠ²ΠΈΡ"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"7 ΠΌΠΈΠ½ΡΡΠΈ ΠΈ 16 ΡΠ΅ΠΊΡΠ½Π΄ΠΈ"}},"simpleText":"7:16"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"ΠΠ° Π³Π»Π΅Π΄Π°Π½Π΅ ΠΏΠΎ-ΠΊΡΡΠ½ΠΎ","toggledTooltip":"ΠΠΎΠ±Π°Π²Π΅Π½","untoggledServiceEndpoint":{"clickTrackingParams":"CJsBEPnnAxgBIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"luVIoGllnac","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CJsBEPnnAxgBIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"luVIoGllnac"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"ΠΠ° Π³Π»Π΅Π΄Π°Π½Π΅ ΠΏΠΎ-ΠΊΡΡΠ½ΠΎ"}},"toggledAccessibility":{"accessibilityData":{"label":"ΠΠΎΠ±Π°Π²Π΅Π½"}},"trackingParams":"CJsBEPnnAxgBIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"ΠΠΎΠ±Π°Π²ΡΠ½Π΅ Π² ΠΎΠΏΠ°ΡΠΊΠ°ΡΠ°","toggledTooltip":"ΠΠΎΠ±Π°Π²Π΅Π½","untoggledServiceEndpoint":{"clickTrackingParams":"CJoBEMfsBBgCIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CJoBEMfsBBgCIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"luVIoGllnac","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CJoBEMfsBBgCIhMIrYCl_9u5jAMVcUZ6BR1JKyrK","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["luVIoGllnac"],"params":"CAQ%3D"}},"videoIds":["luVIoGllnac"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"ΠΠΎΠ±Π°Π²ΡΠ½Π΅ Π² ΠΎΠΏΠ°ΡΠΊΠ°ΡΠ°"}},"toggledAccessibility":{"accessibilityData":{"label":"ΠΠΎΠ±Π°Π²Π΅Π½"}},"trackingParams":"CJoBEMfsBBgCIhMIrYCl_9u5jAMVcUZ6BR1JKyrK"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Π‘Π΅Π³Π° ΡΠ»ΡΡΠ°ΡΠ΅"}]}}}],"accessibility":{"accessibilityData":{"label":"Complex Analysis 11: Laurent Series – 7 ΠΌΠΈΠ½ΡΡΠΈ ΠΈ 16 ΡΠ΅ΠΊΡΠ½Π΄ΠΈ – ΠΡΠΌ ΠΊΠ°Π½Π°Π»Π° – MathsStatsUNSW - 171 Ρ ΠΈΠ». ΠΏΠΎΠΊΠ°Π·Π²Π°Π½ΠΈΡ - ΠΏΡΠ΅Π΄ΠΈ 9 Π³ΠΎΠ΄ΠΈΠ½ΠΈ – ΠΏΡΡΠΊΠ°Π½Π΅ Π½Π° Π²ΠΈΠ΄Π΅ΠΎΠΊΠ»ΠΈΠΏΠ°"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/luVIoGllnac/mqdefault_6s.webp?du=3000 sqp=CMCxtb8G rs=AOn4CLD_HC7FGhLwvj0tRb2Un3sXXg4e9w","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"lockupViewModel":{"contentImage":{"collectionThumbnailViewModel":{"primaryThumbnail":{"thumbnailViewModel":{"image":{"sources":[{"url":"https://i.ytimg.com/vi/r4s3UxIZloI/hqdefault.jpg?sqp=-oaymwEWCKgBEF5IWvKriqkDCQgBFQAAiEIYAQ== rs=AOn4CLClcFJ7gdxJghcxPrvMGN5D6ZH9TQ","width":168,"height":94},{"url":"https://i.ytimg.com/vi/r4s3UxIZloI/hqdefault.jpg?sqp=-oaymwEXCNACELwBSFryq4qpAwkIARUAAIhCGAE= rs=AOn4CLBwJMcjnaprEtSjTDlch14O-Zf2-A","width":336,"height":188}]},"overlays":[{"thumbnailOverlayBadgeViewModel":{"thumbnailBadges":[{"thumbnailBadgeViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAYLISTS"}}]},"text":"25 Π²ΠΈΠ΄Π΅ΠΎΠΊΠ»ΠΈΠΏΠ°","badgeStyle":"THUMBNAIL_OVERLAY_BADGE_STYLE_DEFAULT","backgroundColor":{"lightTheme":984883,"darkTheme":984883}}}],"position":"THUMBNAIL_OVERLAY_BADGE_POSITION_BOTTOM_END"}},{"thumbnailHoverOverlayViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAY_ALL"}}]},"text":{"content":"ΠΡΡΠΊΠ°Π½Π΅ Π½Π° Π²ΡΠΈΡΠΊΠΈ","styleRuns":[{"startIndex":0,"length":17}]},"style":"THUMBNAIL_HOVER_OVERLAY_STYLE_COVER"}}],"backgroundColor":{"lightTheme":1772889,"darkTheme":1772889}}},"stackColor":{"lightTheme":7564185,"darkTheme":8551579}}},"metadata":{"lockupMetadataViewModel":{"title":{"content":"Complex Power Series"},"metadata":{"contentMetadataViewModel":{"metadataRows":[{"metadataParts":[{"text":{"content":"Ranjan Khatu
#############################
