• Title, Summary, Keyword: hypergeometric functions

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NEW TRANSFORMATIONS FOR HYPERGEOMETRIC FUNCTIONS DEDUCIBLE BY FRACTIONAL CALCULUS

  • Kim, Yong Sup
    • Communications of the Korean Mathematical Society
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    • v.33 no.4
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    • pp.1239-1248
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    • 2018
  • Recently, many authors have obtained several hypergeometric identities involving hypergeometric functions of one and multi-variables such as the Appell's functions and Horn's functions. In this paper, we obtain several new transformations suitably by applying the fractional calculus operator to these hypergeometric identities, which was introduced recently by Tremblay.

DECOMPOSITION FORMULAE FOR GENERALIZED HYPERGEOMETRIC FUNCTIONS WITH THE GAUSS-KUMMER IDENTITY

  • Hayashi, Naoya;Matsui, Yutaka
    • Communications of the Korean Mathematical Society
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    • v.29 no.1
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    • pp.97-108
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    • 2014
  • In the theory of special functions, it is important to study some formulae describing hypergeometric functions with other hypergeometric functions. In this paper, we give some methods to obtain a lot of decomposition formulae for generalized hypergeometric functions.

INTEGRAL REPRESENTATIONS FOR SRIVASTAVA'S HYPERGEOMETRIC FUNCTION HA

  • Choi, June-Sang;Hasanov, Anvar;Turaev, Mamasali
    • Honam Mathematical Journal
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    • v.34 no.1
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    • pp.113-124
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    • 2012
  • While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeometric series of the second order, which were denoted by $H_A$, $H_B$ and $H_C$. Each of these three triple hypergeometric functions $H_A$, $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function $H_A$.

INTEGRAL REPRESENTATIONS FOR SRIVASTAVA'S HYPERGEOMETRIC FUNCTION HB

  • Choi, June-Sang;Hasanov, Anvar;Turaev, Mamasali
    • The Pure and Applied Mathematics
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    • v.19 no.2
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    • pp.137-145
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    • 2012
  • While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeometric series of the second order, which were denoted by $H_A$, $H_B$ and $H_C$. Each of these three triple hypergeometric functions $H_A$, $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function $H_B$.

GENERATING FUNCTIONS FOR THE EXTENDED WRIGHT TYPE HYPERGEOMETRIC FUNCTION

  • Jana, Ranjan Kumar;Maheshwari, Bhumika;Shukla, Ajay Kumar
    • Communications of the Korean Mathematical Society
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    • v.32 no.1
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    • pp.75-84
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    • 2017
  • In recent years, several interesting families of generating functions for various classes of hypergeometric functions were investigated systematically. In the present paper, we introduce a new family of extended Wright type hypergeometric function and obtain several classes of generating relations for this extended Wright type hypergeometric function.

Recursion Formulas for Exton's triple Hypergeometric Functions

  • Sahai, Vivek;Verma, Ashish
    • Kyungpook Mathematical Journal
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    • v.56 no.2
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    • pp.473-506
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    • 2016
  • This paper continues the study of recursion formulas of multivariable hypergeometric functions. Earlier, in [4], the authors have given the recursion formulas for three variable Lauricella functions, Srivastava's triple hypergeometric functions and k-variable Lauricella functions. Further, in [5], we have obtained recursion formulas for the general triple hypergeometric function. We present here the recursion formulas for Exton's triple hypergeometric functions.

Certain Fractional Integral Operators and Extended Generalized Gauss Hypergeometric Functions

  • CHOI, JUNESANG;AGARWAL, PRAVEEN;JAIN, SILPI
    • Kyungpook Mathematical Journal
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    • v.55 no.3
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    • pp.695-703
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    • 2015
  • Several interesting and useful extensions of some familiar special functions such as Beta and Gauss hypergeometric functions and their properties have, recently, been investigated by many authors. Motivated mainly by those earlier works, we establish some fractional integral formulas involving the extended generalized Gauss hypergeometric function by using certain general pair of fractional integral operators involving Gauss hypergeometric function $_2F_1$, Some interesting special cases of our main results are also considered.

INTEGRAL REPRESENTATIONS FOR SRIVASTAVA'S HYPERGEOMETRIC FUNCTION HC

  • Choi, Junesang;Hasanov, Anvar;Turaev, Mamasali
    • Honam Mathematical Journal
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    • v.34 no.4
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    • pp.473-482
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    • 2012
  • While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeo-metric series of the second order, which were denoted by $H_A$, $H_B$ and $H_C$. Each of these three triple hypergeometric functions $H_A$, $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function $H_C$.

EXTENDED HYPERGEOMETRIC FUNCTIONS OF TWO AND THREE VARIABLES

  • AGARWAL, PRAVEEN;CHOI, JUNESANG;JAIN, SHILPI
    • Communications of the Korean Mathematical Society
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    • v.30 no.4
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    • pp.403-414
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    • 2015
  • Extensions of some classical special functions, for example, Beta function B(x, y) and generalized hypergeometric functions $_pF_q$ have been actively investigated and found diverse applications. In recent years, several extensions for B(x, y) and $_pF_q$ have been established by many authors in various ways. Here, we aim to generalize Appell's hypergeometric functions of two variables and Lauricella's hypergeometric function of three variables by using the extended generalized beta type function $B_p^{({\alpha},{\beta};m)}$ (x, y). Then some properties of the extended generalized Appell's hypergeometric functions and Lauricella's hypergeometric functions are investigated.

Generalized Incomplete Pochhammer Symbols and Their Applications to Hypergeometric Functions

  • Sahai, Vivek;Verma, Ashish
    • Kyungpook Mathematical Journal
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    • v.58 no.1
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    • pp.67-79
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    • 2018
  • In this paper, we present new generalized incomplete Pochhammer symbols and using this we introduce the extended generalized incomplete hypergeometric functions. We derive certain properties, generating functions and reduction formulas of these extended generalized incomplete hypergeometric functions. Special cases of this extended generalized incomplete hypergeometric functions are also discussed.