DLMF:18.5.E9 (Q5517): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
 
imported>Admin
Property / Symbols used
 
Property / Symbols used: Q11581 / rank
 
Normal rank
Property / Symbols used: Q11581 / qualifier
 
test:

F 1 2 ( a , b ; c ; z ) Gauss-hypergeometric-F-as-2F1 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}

\genhyperF{2}{1}@{\NVar{a},\NVar{b}}{\NVar{c}}{\NVar{z}}
Property / Symbols used: Q11581 / qualifier
 
xml-id: C16.S2.m5abdec

Revision as of 14:16, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:18.5.E9
No description defined

    Statements

    C n ( λ ) ( x ) = ( 2 λ ) n n ! F 1 2 ( - n , n + 2 λ λ + 1 2 ; 1 - x 2 ) , ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 Pochhammer 2 𝜆 𝑛 𝑛 Gauss-hypergeometric-F-as-2F1 𝑛 𝑛 2 𝜆 𝜆 1 2 1 𝑥 2 {\displaystyle{\displaystyle C^{(\lambda)}_{n}\left(x\right)=\frac{{\left(2% \lambda\right)_{n}}}{n!}{{}_{2}F_{1}}\left({-n,n+2\lambda\atop\lambda+\tfrac{1% }{2}};\frac{1-x}{2}\right),}}
    0 references
    0 references
    F 1 2 ( a , b ; c ; z ) Gauss-hypergeometric-F-as-2F1 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}
    C16.S2.m5abdec
    0 references