Investigation of properties of $r$-generalized hypergeometric functions
DOI:
https://doi.org/10.20535/mmtu-2019.1-005Keywords:
Generalized hypergeometric function, Confluent hypergeometric function, Beta-function, Fractional integral operators of SaigoAbstract
The aim of paper is to study the properties of the new $r$-generalized hypergeometric and $r$-generalized beta functions. In the study were used the common methods of the theory of special functions, the theory of integral transforms and operators of fractional integration. We obtained relations for new introduced functions with fractional integral operators of Saigo. We used the concept of Hadamard product of power series in our investigation. Also there was establish formula for beta-transform of new $r$-generalized hypergeometric function. Integral transforms and fractional integral formulas involving hypergeometric function are interesting by themselves and play important roles in applications. These results can be used for further development of the theory of special functions and it widespread use.References
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