Some formulae for double Clausenian functions. (English) Zbl 0953.33010

The author derives reduction and transformation formulae for certain Kampé de Fériet functions from an Euler integral representation. A simple example case is given by formula (13): \[ F^{1:2;2}_{2:0;0}\left[\begin{matrix} a &b,&c &b',&c'\\ b+b',&c+c'& -;& -\end{matrix}\Bigl|x,{x\over x-1}\right]={_2F_1}\left[\begin{matrix} a,&b \\ b+b'\end{matrix}\Bigr|x\right]{_2F_1}\left[\begin{matrix} a,&c'\\ c+c'\end{matrix}\Bigl|{x \over x-1}\right].\Bigr. \]


33C70 Other hypergeometric functions and integrals in several variables
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