Formula:6646

Digital Library of Mathematical Functions ID 18.26.E20

${\displaystyle{\displaystyle{{}_{2}F_{1}}\left({-y,-y+\beta-\gamma\atop\beta+\delta+1};z\right){{}_{2}F_{1}}\left({y-N,y+\gamma+1\atop-\delta-N};z\right)=\sum_{n=0}^{N}\frac{{\left(-N\right)_{n}}{\left(\gamma+1\right)_{n}}}{{\left(-\delta-N\right)_{n}}n!}R_{n}\left(y(y+\gamma+\delta+1);-N-1,\beta,\gamma,\delta\right)z^{n}.}}$

Symbols List

• ${\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$: = F ( a , b ; c ; z ) notation for Gauss’ hypergeometric function
• ${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$:
• ${\displaystyle{\displaystyle R_{\NVar{n}}\left(\NVar{x};\NVar{\alpha},\NVar{\beta},\NVar{\gamma},\right)\)\@add@PDF@RDFa@triples\end{document}}}$: Racah polynomial
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle y}}$: real variable
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle N}}$: positive integer
• ${\displaystyle{\displaystyle\delta}}$: arbitary small positive constant
 

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