Euler-type transformations for the generalized hypergeometric function \(_{r+2} F _{r+1}(x)\)
The authors provide generalizations of two of Euler's classical transformation formulas for the Gauss hypergeometric function extended to the case of the generalized hypergeometric function \(_{r+2}F_{r+1}(x)\) when there are additional numerator and denominator parameters differing by unity. The method employed to deduce the latter is also implemented to obtain a Kummer-type transformation formula for \(_{r+1}F_{r+1}(x)\).
scientific article; zbMATH DE number 5947336
scientific article