Abstract
Various extensions of the beta function together with their associated extended hypergeometric and confluent hypergeometric
functions have been introduced and investigated. In this paper, using the very recently contrived extended beta function, we aim to introduce an extension
F
v
p
,
q
;
λ
;
σ
,
τ
u
{{}_{u}F_{v}^{p,q;\lambda;\sigma,\tau}}
of the generalized hypergeometric function
F
v
u
{{}_{u}F_{v}}
and investigate certain classes of transforms and several identities of a generalized probability distribution involving this extension. In fact, we present
some interesting formulas of Jacobi, Gegenbauer, pathway, Laplace, and Legendre transforms of
this extension multiplied by a polynomial. We also introduce a generalized probability distribution to investigate its several related properties.
Further, we consider some special cases of our main results with an argument about the derived process of a known result.
Automated correlation dimension analysis of optically injected solid state lasers
