Recurrent identities for two special functions of hypergeometric type - Svetlana V. Podkletnova (Вестник Самарского университета: Естественнонаучная серия)
The article presents conclusions and proofs of Gauss-type identities for two known hypergeometric type functions. For the derivation and justification of formulas, the representation of functions in the form of a series is used, as well as an integral representation of the functions under consideration. The article uses the definition and properties of gamma and beta functions, the hypergeometric Gauss function, as well as known identities for these functions. Hypergeometric functions are widely used in solving various types of differential equations. The presence of identities connecting the functions involved in the resulting formulas of solutions greatly simplifies both the final formulas and intermediate calculations in many problems related to solving hyperbolic, elliptic and mixed types of equations.