Some improper integrals with integration inﬁnity limit involving generalizad hypergeometric function 2R1(a, b; c; τ ; z) (2007)
In 1991 M. Dotsenko presented a generalization of the Gage hypergeometric function denoted by 2Rτ1 (z), also establishing both its serial representation and its integral representation. It is important to note that in 1999 Nina Virchenko and then, in 2003, Leda Galué considered this function, introducing a set of recurrence and differentiation formulas which simplify some complicated calculations. Kalla and collaborators studied this function and presented a new unified form of the Gamma function, then in 2006, Castillo and collaborators presented some simple representations for this function. In this paper some improper integrals are established with infinite integration limits that involve the generalization τ of the hypergeometric function of Gauss 2R1 (a, b; c; τ; z).