scholarly journals Further Extension of the Generalized Hurwitz-Lerch Zeta Function of Two Variables

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 48
Author(s):  
Kottakkaran Sooppy Nisar
Keyword(s):  
Zeta Function ◽  
Hypergeometric Function ◽  
Summation Formula ◽  
Integral Representations ◽  
Generalized Hypergeometric Function ◽  
Special Cases ◽  
Lerch Zeta Function ◽  
Function Of Two Variables

The main aim of this paper is to provide a new generalization of Hurwitz-Lerch Zeta function of two variables. We also investigate several interesting properties such as integral representations, summation formula, and a connection with the generalized hypergeometric function. To strengthen the main results we also consider some important special cases.

scholarly journals An extension of the generalized Hurwitz-Lerch Zeta function of two variables

Filomat ◽  
2017 ◽  
Vol 31 (1) ◽  
pp. 91-96 ◽  
Author(s):  
Junesang Choi ◽  
Rakesh Parmar
Keyword(s):  
Zeta Function ◽  
Zeta Functions ◽  
Summation Formula ◽  
Integral Representations ◽  
Contour Integral ◽  
Functions Of Two Variables ◽  
Special Cases ◽  
Lerch Zeta Function ◽  
Function Of Two Variables

The main object of this paper is to introduce a new extension of the generalized Hurwitz-Lerch Zeta functions of two variables. We then systematically investigate such its several interesting properties and related formulas as (for example) various integral representations, which provide certain new and known extensions of earlier corresponding results, a summation formula and Mellin-Barnes type contour integral representations. We also consider some important special cases.

scholarly journals A (p,v)-Extension of Hurwitz-Lerch Zeta Function and its Properties

2018 ◽  
Author(s):  
Gauhar Rahman ◽  
KS Nisar ◽  
Shahid Mubeen
Keyword(s):  
Zeta Function ◽  
Beta Function ◽  
Integral Representations ◽  
Basic Properties ◽  
Mellin Transformation ◽  
Special Cases ◽  
Lerch Zeta Function ◽  
Derivative Formulas ◽  
Generating Relations

In this paper, we define a (p,v)-extension of Hurwitz-Lerch Zeta function by considering an extension of beta function defined by Parmar et al. [J. Classical Anal. 11 (2017) 81–106]. We obtain its basic properties which include integral representations, Mellin transformation, derivative formulas and certain generating relations. Also, we establish the special cases of the main results.

scholarly journals Note on the Hurwitz–Lerch Zeta Function of Two Variables

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1431
Author(s):  
Junesang Choi ◽  
Recep Şahin ◽  
Oğuz Yağcı ◽  
Dojin Kim
Keyword(s):  
Zeta Function ◽  
Generating Functions ◽  
Recurrence Relations ◽  
Zeta Functions ◽  
Integral Representations ◽  
Lerch Zeta Function ◽  
Derivative Formulas ◽  
The One ◽  
Function Of Two Variables

A number of generalized Hurwitz–Lerch zeta functions have been presented and investigated. In this study, by choosing a known extended Hurwitz–Lerch zeta function of two variables, which has been very recently presented, in a systematic way, we propose to establish certain formulas and representations for this extended Hurwitz–Lerch zeta function such as integral representations, generating functions, derivative formulas and recurrence relations. We also point out that the results presented here can be reduced to yield corresponding results for several less generalized Hurwitz–Lerch zeta functions than the extended Hurwitz–Lerch zeta function considered here. For further investigation, among possibly various more generalized Hurwitz–Lerch zeta functions than the one considered here, two more generalized settings are provided.

scholarly journals On a Certain Extension of the Hurwitz-Lerch Zeta Function

2014 ◽  
Vol 52 (2) ◽  
Author(s):  
Rakesh K. Parmar ◽  
R. K. Raina
Keyword(s):  
Zeta Function ◽  
Probability Distributions ◽  
Integral Representations ◽  
Mellin Transforms ◽  
Special Cases ◽  
Lerch Zeta Function ◽  
Generating Relations

AbstractOur purpose in this paper is to consider a generalized form of the extended Hurwitz-Lerch Zeta function. For this extended Hurwitz-Lerch Zeta function, we obtain some classical properties which includes various integral representations, a differential formula, Mellin transforms and certain generating relations. We further consider an application to probability distributions and also point out some important special cases of the main results.

scholarly journals Hurwitz Zeta Function of Two Variables and Associated Properties

2020 ◽  
pp. 297-315
Author(s):  
M. A. Pathan ◽  
Maged G. Bin-Saad ◽  
J. A. Younis
Keyword(s):  
Zeta Function ◽  
Integral Representations ◽  
Hurwitz Zeta Function ◽  
Summation Formulas ◽  
Lerch Zeta Function ◽  
Function Of Two Variables

The main objective of this work is to introduce a new generalization of Hurwitz-Lerch zeta function of two variables. Also, we investigate several interesting properties such as integral representations, operational connections and summation formulas.

scholarly journals A New Class of Integrals Involving Generalized Hypergeometric Function and Multivariable Aleph-Function

2020 ◽  
Vol 44 (4) ◽  
pp. 539-550
Author(s):  
DINESH KUMAR ◽  
FRÉDÉRIC AYANT ◽  
DEVENDRA KUMAR
Keyword(s):  
Hypergeometric Function ◽  
Summation Formula ◽  
Generalized Hypergeometric Function ◽  
New Class ◽  
Special Cases

The aim of this paper is to evaluate an interesting integral involving generalized hypergeometric function and the multivariable Aleph-function. The integral is evaluated with the help of an integral involving generalized hypergeometric function obtained recently by Kim et al. [?]. The integral is further used to evaluate an interesting summation formula concerning the multivariable Aleph-function. A few interesting special cases and corollaries have also been discussed.

scholarly journals Some Integral Results Associated with Generalized Hypergeometric Function

2019 ◽  
Vol 8 (2) ◽  
pp. 1067-1071
Keyword(s):  
Orthogonal Polynomials ◽  
Hypergeometric Function ◽  
Integral Representations ◽  
Generalized Hypergeometric Function ◽  
Classical Orthogonal Polynomials ◽  
Different Types ◽  
Function Of Two Variables

In previous papers, it has been introduced a generalized hypergeometric function of two variables. The present paper aims at to derive different types of integral representations for the generalized hypergeometric function. The results derived here are very general in nature and are interesting and can obtain some known and new integrals for various polynomials. Each result is followed by its applications to the classical orthogonal polynomials.

scholarly journals Integral representations of generalized Lauricella hypergeometric functions

1992 ◽  
Vol 15 (4) ◽  
pp. 653-657 ◽  
Author(s):  
Vu Kim Tuan ◽  
R. G. Buschman
Keyword(s):  
Integral Representation ◽  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Integral Representations ◽  
Generalized Hypergeometric Function ◽  
Appell Function

The generalized hypergeometric function was introduced by Srivastava and Daoust. In the present paper a new integral representation is derived. Similarly new integral representations of Lauricella and Appell function are obtained.

Extended Mittag-Leffler function and associated fractional calculus operators

2020 ◽  
Vol 27 (2) ◽  
pp. 199-209 ◽  
Author(s):  
Junesang Choi ◽  
Rakesh K. Parmar ◽  
Purnima Chopra
Keyword(s):  
Fractional Calculus ◽  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Fractional Integrals ◽  
Generalized Hypergeometric Function ◽  
Pochhammer Symbol ◽  
Special Cases ◽  
Fractional Calculus Operators ◽  
Fractional Integrals And Derivatives ◽  
Appl Math

AbstractMotivated mainly by certain interesting recent extensions of the generalized hypergeometric function [H. M. Srivastava, A. Çetinkaya and I. Onur Kıymaz, A certain generalized Pochhammer symbol and its applications to hypergeometric functions, Appl. Math. Comput. 226 2014, 484–491] by means of the generalized Pochhammer symbol, we introduce here a new extension of the generalized Mittag-Leffler function. We then systematically investigate several properties of the extended Mittag-Leffler function including some basic properties, Mellin, Euler-Beta, Laplace and Whittaker transforms. Furthermore, certain properties of the Riemann–Liouville fractional integrals and derivatives associated with the extended Mittag-Leffler function are also investigated. Some interesting special cases of our main results are pointed out.

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