Some improper integrals with integration infinity limit involving generalizad hypergeometric function 2R1(a, b; c; τ ; z)

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Jaime Castillo Pérez

Keywords

generalized hypergeometric function, improper integrals.

Abstract

In 1991 M. Dotsenko presented a generalization of Gauss’ hypergeometric function refered as 2Rτ1(z), and established its representation in series and integral. It is important to remark that in 1999 Nina Virchenko and, later in 2003, Leda Galu´e considered this function by introducing a set of recurrence and differentiation formulas; they permit simplify some complicated calculus. Kalla et al estudied this function and they presented a new unified form of the gamma function. Later in 2006, Castillo et al present some simple representation for this function. Along this paper work some improper integrals with integration infinity limit involving generalized hypergeometric function
2R1(a, b; c; τ ; z) are displayed.

MSC: 33D15, 33D90, 33D60, 34M03,  62E15

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