Abstract
In this paper, we investigate some properties of the Pochhammer
p
,
s
,
k
-symbol
ξ
n
,
k
,
s
p
and gamma
p
,
s
,
k
-function
Γ
s
,
k
p
ξ
. We then prove several identities for newly defined symbol
ξ
n
,
k
,
s
p
and the function
Γ
s
,
k
p
ξ
. The integral representations for the gamma
p
,
s
,
k
-function and beta
p
,
s
,
k
-function are presented. Also, we define a new Mittag-Leffler
p
,
s
,
k
-function and study its analytic properties and its transforms.