3,420 research outputs found
Generalized fractional operator representations of Jacobi type orthogonal polynomials
The aim of this paper is to apply generalized operators of fractional
integration and differentiation involving Appell's function due to
Marichev-Saigo-Maeda (MSM), to the Jacobi type orthogonal polynomials. The
results are expressed in terms of generalized hypergeometric function. Some of
the interesting special cases of the main results also established
Marichev-Saigo-Maeda fractional operator representations of generalized Struve function
The aim of this paper is to apply generalized operators of fractional
integration and differentiation involving Appells function due to
Marichev-Saigo-Maeda, to the generalized Struve function. The results are
expressed in terms of generalized Wright function. The results obtained here
are general in nature and can easily obtain various known results
Some unified integrals associated with Bessel-Struve kernel function
In this paper, we discuss the generalized integral formula involving
Bessel-Struve kernel function , which
expressed in terms of generalized Wright functions. Many interesting special
cases also obtained in this study.Comment: 8 page
Marichev-Saigo-Maeda fractional integration operators of generalized Bessel functions
Two integral operator involving the Appell's functions, or Horn's function in
the kernel are considered. Composition of such functions with generalized
Bessel functions of the first kind are expressed in term of generalized Wright
function and generalized hypergeometric series. Many special cases, including
cosine and sine function are also discussed.Comment: 13 page
Unified integral operator involving generalized Bessel-Maitland function
The main object of this article is to present an interesting double integral
involving generalized Bessel-Maitland function defined by Ghaysuddin et al.,
which is expressed in terms of generalized (Wright) hypergeometric function. We
also considered some special cases as an application of the main result
Composition formulas of Bessel-Struve kernel function
The generalized operators of fractional integration involving Appell's
function due to Marichev-Saigo-Maeda, is applied to the Bessel
Struve kernel function to obtain the results in terms of generalized Wright functions.The
pathway integral representations Bessel Struve kernel function and its relation
between many other functions also derived in this study.Comment: 13 page
-Whittaker function and associated properties and formulas
Recently, various extensions and variants of Bessel functions of several
kinds have been presented. Among them, the -confluent hypergeometric
function has been introduced and investigated. Here, we aim to
introduce an extended -Whittaker function by using the function
and establish its various properties and associated formulas such
as integral representations, some transformation formulas and differential
formulas. Relevant connections of the results presented here With those
involving relatively simple Whittaker functions are also pointed out
A New Class of Integrals Involving Extended Hypergeometric Function
Our purpose in this present paper is to investigate generalized integration
formulas containing the extended generalized hypergeometric function and
obtained results are expressed in terms of extended hypergeometric function.
Certain special cases of the main results presented here are also pointed out
for the extended Gauss' hypergeometric and confluent hypergeometric functions
Some Unified Integrals Associated with Generalized Bessel-Maitland Function
Generalized integral formulas involving the generalized Bessel-Maitland
function are considered and it expressed in terms of generalized Wright
hypergeometric functions. By assuming appropriate values of the parameters in
the main results, we obtained some interesting results of ordinary Bessel
function
Inequalities of extended (p,q)-beta and confluent hypergeometric function
In this present paper, we establish the log-convexity and Tur\'an type
inequalities of extended -beta functions. Also, we present the
log-convexity, the monotonicity and Tur\'an type inequalities for extended
-confluent hypergeometric function by using the inequalities of extended
-beta functions.Comment: 9 page
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