Deprecated: $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372
DLMF:15.4.E16 - MaRDI portal

DLMF:15.4.E16 (Q5697)

From MaRDI portal
No description defined
Language Label Description Also known as
English
DLMF:15.4.E16
No description defined

    Statements

    DLMF defining formula
    F ⁡ ( a , 1 - a ; 3 2 ; sin 2 ⁡ z ) = sin ⁡ ( ( 2 ⁢ a - 1 ) ⁢ z ) ( 2 ⁢ a - 1 ) ⁢ sin ⁡ z . Gauss-hypergeometric-F 𝑎 1 𝑎 3 2 2 𝑧 2 𝑎 1 𝑧 2 𝑎 1 𝑧 {\displaystyle{\displaystyle F\left(a,1-a;\tfrac{3}{2};{\sin^{2}}z\right)=% \frac{\sin\left((2a-1)z\right)}{(2a-1)\sin z}.}}
    0 references
    Symbols used
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    DLMF defining formula
    F ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}
    xml-id
    C15.S2.E1.m2aodec
    0 references
    sine function
    DLMF defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2acdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1odec
    0 references
    real or complex parameter
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1jdec
    0 references

    Identifiers

     
    Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Item:Q5697&oldid=24173047"
    Powered by MediaWiki