On the integral representations for the confluent hypergeometric function | Zendy

Bujar Xh. Fejzullahu | Zendy

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On the integral representations for the confluent hypergeometric function

Author(s) -

Bujar Xh. Fejzullahu

Publication year - 2016

Publication title -

proceedings of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

eISSN - 1471-2946

pISSN - 1364-5021

DOI - 10.1098/rspa.2016.0421

Subject(s) - generalized hypergeometric function , confluent hypergeometric function , basic hypergeometric series , hypergeometric identity , hypergeometric function , barnes integral , mathematics , hypergeometric function of a matrix argument , methods of contour integration , bilateral hypergeometric series , pure mathematics , function (biology) , representation (politics) , hypergeometric distribution , identity (music) , mathematical analysis , algebra over a field , physics , evolutionary biology , biology , politics , political science , acoustics , law

In this paper, we derive a new contour integral representation for the confluent hypergeometric function as well as for its various special cases. Consequently, we derive expansions of the confluent hypergeometric function in terms of functions of the same kind. Furthermore, we obtain a new identity involving integrals and sums of confluent hypergeometric functions. Our results generalized several well-known results in the literature.

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