ABSTRACT
Chapter 7
HYPERGEOMETRIC TYPE INTEGRAL
TRANSFORMS ON THE SPACE L
;r
7.1. Laplace Type Transforms
We consider the integral transform
L
;k
f
(x) =
Z
(xt)
e
(xt)
k
f(t)dt (7.1.1)
with 2 C and k > 0. This is a modication of the generalized Laplace transform L
k;
given
in (3.3.3):
L
;k
f
(x) = k
=k
W
k
1=k
L
1=k;
f
(x) = k
=k
L
1=k;
f
k
1=k
x
; (7.1.2)
where the operator W
is dened by (3.3.12).
