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In 1991 M. Dotsenko presented a generalization of Gauss' hypergeometric function refered as 2R1τ (z), and established its representation in series and integral. It is important to remark that in 1999 Nina Virchenko and, later in 2003, Leda Galué 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. [ABSTRACT FROM AUTHOR]