  We introduce a gamma function $\Ga(x,z)$ in two complex variables which
extends the classical gamma function $\Ga(z)$ in the sense that $\lim_{x\to
1}\Ga(x,z)=\Ga(z)$. 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.

Number Theory