[3.2.3.1] The general -function is defined as the inverse
Mellin transform [24]
![]() |
(A.1) |
where the contour runs from
to
separating
the poles of
from those of
.
[3.2.3.2] Empty products are interpreted as
unity.
[3.2.3.3] The integers
satisfy
and
.
[3.2.3.4] The coefficients
and
are positive real numbers and the complex
parameters
are such that no poles in the integrand coincide.
[3.2.3.5] If
![]() |
(A.2) |
[page 4, §0]
then the integral converges absolutely and defines the -function in
the sector
.
[4.1.0.1] The
-function is also well
defined when either
![]() |
(A.3) |
or
![]() |
(A.4) |
[4.1.0.2] For the
-function has the series representation
![]() |
(A.5) |
provided that for
and
[4.1.0.3] The
-function is a generalization of Meijers
-function and
many of the known special functions are special cases of it.