A gamma function in two variables

2013/05/09 by Bachraoui, Mohamed El
#11M06 #11Y60 #33B15 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1305.2174

Abstract

We introduce a gamma function \Ga(x,z) in two complex variables which extends the classical gamma function \Ga(z) in the sense that lim_{x→ 1}\Ga(x,z)=\Ga(z). We will show that many properties which \Ga(z) enjoys extend in a natural way to the function \Ga(x,z). Among other things we shall provide functional equations, a multiplication formula, and analogues of the Stirling formula with asymptotic estimates as consequences.

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