INTEGRAL TRANSFORM OF K4-FUNCTION

2021 ◽  
Vol 21 (2) ◽  
pp. 429-436
Author(s):  
SEEMA KABRA ◽  
HARISH NAGAR
Keyword(s):  
Laplace Transform ◽  
Hypergeometric Function ◽  
Integral Transform ◽  
Integral Transforms ◽  
Gauss Hypergeometric Function ◽  
Wright Function ◽  
Generalized Wright Function ◽  
Special Cases ◽  
Euler Transform

In this present work we derived integral transforms such as Euler transform, Laplace transform, and Whittaker transform of K4-function. The results are given in generalized Wright function. Some special cases of the main result are also presented here with new and interesting results. We further extended integral transforms derived here in terms of Gauss Hypergeometric function.

scholarly journals Computation of certain integral formulas involving generalized Wright function

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Nabiullah Khan ◽  
Talha Usman ◽  
Mohd Aman ◽  
Shrideh Al-Omari ◽  
Serkan Araci
Keyword(s):  
Hypergeometric Function ◽  
Special Functions ◽  
Gaussian Quadrature ◽  
Integral Transforms ◽  
Wright Function ◽  
Gaussian Quadrature Formula ◽  
Integral Formulas ◽  
Generalized Wright Function ◽  
Special Cases ◽  
Generalized Wright Hypergeometric Function

Abstract The aim of the paper is to derive certain formulas involving integral transforms and a family of generalized Wright functions, expressed in terms of the generalized Wright hypergeometric function and in terms of the generalized hypergeometric function as well. Based on the main results, some integral formulas involving different special functions connected with the generalized Wright function are explicitly established as special cases for different values of the parameters. Moreover, a Gaussian quadrature formula has been used to compute the integrals and compare with the main results by using graphical representations.

scholarly journals The H-function transform

1970 ◽  
Vol 11 (2) ◽  
pp. 142-148 ◽  
Author(s):  
K. C. Gupta ◽  
P. K. Mittal
Keyword(s):  
Laplace Transform ◽  
Inversion Formula ◽  
Integral Transform ◽  
Applied Mathematics ◽  
Integral Transforms ◽  
Hankel Transform ◽  
Stieltjes Transform ◽  
Special Cases ◽  
Mathematics And Physics

Here we introduce a new integral transform whose kernel is the H-function. Since most of the important functions occurring in Applied Mathematics and Physics are special cases of the H-function, various integral transforms involving these functions as kernels follow as special cases of our transform. We mention some of them here and observe that a study of this transform gives general and useful results which serve as key formulae for several important integral transforms viz. Laplace transform, Hankel transform. Stieltjes transform and the various generalizations of these transforms. In the end we establish an inversion formula for the new transform and point out its special cases which are generalizations of results found recently.

scholarly journals On Fractional Integral Inequalities Involving Hypergeometric Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
D. Baleanu ◽  
S. D. Purohit ◽  
Praveen Agarwal
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Gauss Hypergeometric Function ◽  
Liouville Type ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Chebyshev Functional

Here we aim at establishing certain new fractional integral inequalities involving the Gauss hypergeometric function for synchronous functions which are related to the Chebyshev functional. Several special cases as fractional integral inequalities involving Saigo, Erdélyi-Kober, and Riemann-Liouville type fractional integral operators are presented in the concluding section. Further, we also consider their relevance with other related known results.

scholarly journals Certain Integral Transform and Fractional Integral Formulas for the Generalized Gauss Hypergeometric Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Junesang Choi ◽  
Praveen Agarwal
Keyword(s):  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Integral Transform ◽  
Special Functions ◽  
Integral Transforms ◽  
Integral Formulas ◽  
Special Cases

A remarkably large number of integral transforms and fractional integral formulas involving various special functions have been investigated by many authors. Very recently, Agarwal gave some integral transforms and fractional integral formulas involving theFp(α,β)(·). In this sequel, using the same technique, we establish certain integral transforms and fractional integral formulas for the generalized Gauss hypergeometric functionsFp(α,β,m)(·). Some interesting special cases of our main results are also considered.

scholarly journals Geometric properties of some linear operators defined by convolution

2008 ◽  
Vol 39 (4) ◽  
pp. 325-334 ◽  
Author(s):  
R. Aghalary ◽  
A. Ebadian ◽  
S. Shams
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Integral Transform ◽  
Integral Transforms ◽  
Linear Operators ◽  
Geometric Properties ◽  
Special Cases ◽  
Classical Integral ◽  
Alpha Beta

Let $\mathcal{A}$ denote the class of normalized analytic functions in the unit disc $ U $ and $ P_{\gamma} (\alpha, \beta) $ consists of $ f \in \mathcal{A} $ so that$ \exists ~\eta \in \mathbb{R}, \quad \Re \bigg \{e^{i\eta} \bigg [(1-\gamma) \Big (\frac{f(z)}{z}\Big )^{\alpha}+ \gamma \frac{zf'(z)}{f(z)} \Big (\frac{f(z)}{z}\Big )^{\alpha} - \beta\bigg ]\bigg \} > 0. $ In the present paper we shall investigate the integral transform$ V_{\lambda, \alpha}(f)(z) = \bigg \{\int_{0}^{1} \lambda(t) \Big (\frac{f(tz)}{t}\Big )^{\alpha}dt\bigg \}^{\frac{1}{\alpha}}, $ where $ \lambda $ is a non-negative real valued function normalized by $ \int_{0}^{1}\lambda(t) dt=1 $. Actually we aim to find conditions on the parameters $ \alpha, \beta, \gamma, \beta_{1}, \gamma_{1} $ such that $ V_{\lambda, \alpha}(f) $ maps $ P_{\gamma}(\alpha, \beta) $ into $ P_{\gamma_{1}}(\alpha, \beta_{1}) $. As special cases, we study various choices of $ \lambda(t) $, related to classical integral transforms.

Integral transforms and probability distributions involving a generalized hypergeometric function

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nabiullah Khan ◽  
Talha Usman ◽  
Mohd Aman ◽  
Shrideh Al-Omari ◽  
Junesang Choi
Keyword(s):  
Probability Distribution ◽  
Hypergeometric Function ◽  
Probability Distributions ◽  
Beta Function ◽  
Integral Transforms ◽  
Generalized Hypergeometric Function ◽  
Confluent Hypergeometric Functions ◽  
Special Cases ◽  
Legendre Transforms ◽  
Generalized Probability

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.

On a family of the incomplete H-functions and associated integral transforms

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Manish Kumar Bansal ◽  
Devendra Kumar
Keyword(s):  
Integral Transform ◽  
Special Functions ◽  
Natural Extension ◽  
Integral Transforms ◽  
Legendre Transform ◽  
Physical Sciences ◽  
Special Cases ◽  
Improper Integrals ◽  
Jacobi Transform ◽  
Math Phys

Abstract Recently, Srivastava, Saxena and Parmar [H. M. Srivastava, R. K. Saxena and R. K. Parmar, Some families of the incomplete H-functions and the incomplete H ¯ {\overline{H}} -functions and associated integral transforms and operators of fractional calculus with applications, Russ. J. Math. Phys. 25 2018, 1, 116–138] suggested incomplete H-functions (IHF) that paved the way to a natural extension and decomposition of H-function and other connected functions as well as to some important closed-form portrayals of definite and improper integrals of different kinds of special functions of physical sciences. In this article, our key aim is to present some new integral transform (Jacobi transform, Gegenbauer transform, Legendre transform and 𝖯 δ {\mathsf{P}_{\delta}} -transform) of this family of incomplete H-functions. Further, we give several interesting new and known results which are special cases our key results.

scholarly journals On Mathieu-type series for the unified Gaussian hypergeometric functions

2020 ◽  
Vol 14 (1) ◽  
pp. 138-149
Author(s):  
Rakesh Parmar ◽  
Tibor Pogány
Keyword(s):  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Integral Form ◽  
Type A ◽  
Gauss Hypergeometric Function ◽  
Type Series ◽  
Gaussian Hypergeometric Functions ◽  
Special Cases

The main purpose of this paper is to present closed integral form expressions for the Mathieu-type a-series and for the associated alternating versions whose terms contain a generalized p-extended Gauss' hypergeometric function. Related bounding inequalities for the p-generalized Mathieu-type series are also obtained. Finally, a set of various (known or new) special cases and consequences of the results earned are presented.

scholarly journals Fractional Calculus of the Extended Hypergeometric Function

2020 ◽  
Vol 5 (1) ◽  
pp. 369-384
Author(s):  
Recep Şahin ◽  
Oğuz Yağcı
Keyword(s):  
Kinetic Equation ◽  
Fractional Calculus ◽  
Fractional Derivative ◽  
Hypergeometric Function ◽  
Generating Functions ◽  
Integral Transforms ◽  
Gauss Hypergeometric Function ◽  
Fractional Kinetic Equation ◽  
Fractional Derivative Operators

AbstractHere, our aim is to demonstrate some formulae of generalization of the extended hypergeometric function by applying fractional derivative operators. Furthermore, by applying certain integral transforms on the resulting formulas and develop a new futher generalized form of the fractional kinetic equation involving the generalized Gauss hypergeometric function. Also, we obtain generating functions for generalization of extended hypergeometric function..

scholarly journals ASYMPTOTICS OF A GAUSS HYPERGEOMETRIC FUNCTION WITH TWO LARGE PARAMETERS: A NEW CASE

2019 ◽  
pp. 1-7
Author(s):  
J. F. HARPER
Keyword(s):  
Fluid Mechanics ◽  
Hypergeometric Function ◽  
Recent Work ◽  
Asymptotic Expansions ◽  
Negative Integer ◽  
Gauss Hypergeometric Function ◽  
Special Cases ◽  
Leading Term ◽  
Branch Cut

Asymptotic expansions of the Gauss hypergeometric function with large parameters, $F(\unicode[STIX]{x1D6FC}+\unicode[STIX]{x1D716}_{1}\unicode[STIX]{x1D70F},\unicode[STIX]{x1D6FD}+\unicode[STIX]{x1D716}_{2}\unicode[STIX]{x1D70F};\unicode[STIX]{x1D6FE}+\unicode[STIX]{x1D716}_{3}\unicode[STIX]{x1D70F};z)$ as $|\unicode[STIX]{x1D70F}|\rightarrow \infty$ , are known for many special cases, but not for one that the author encountered in recent work on fluid mechanics: $\unicode[STIX]{x1D716}_{2}=0$ and $\unicode[STIX]{x1D716}_{3}=\unicode[STIX]{x1D716}_{1}z$ . This paper gives the leading term for that case if $\unicode[STIX]{x1D6FD}$ is not a negative integer and $z$ is not on the branch cut $[1,\infty )$ , and it shows how subsequent terms can be found.

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