  In this paper, we introduce a way to generalize the Euler's gamma function as
well as some related special functions. With a given polynomial in one variable
$f(t)\ge 0$, we can associate a function, so-called "gamma function associated
with $f$", defined by $\Gamma_f(s) := \int_0^\infty f^{s-1} e^{-t} dt$. This
function has many features similar to the Euler's gamma function. We also
present some initial results on the gamma-type functional equation for
$\Gamma_f(s)$ in some special cases.
