Abstract
We introduce a gamma function Γ(x, z) in two complex variables which extends the classical gamma function Γ(z) in the sense that lim x→1Γ(x, z) =Γ (z). We will show that many properties which Γ(z) enjoys extend in a natural way to the function Γ(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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