• 제목/요약/키워드: Gauss hypergeometric functions

검색결과 43건 처리시간 0.022초

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

  • Hayashi, Naoya;Matsui, Yutaka
    • 대한수학회논문집
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    • 제29권1호
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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.

Certain Fractional Integral Operators and Extended Generalized Gauss Hypergeometric Functions

  • CHOI, JUNESANG;AGARWAL, PRAVEEN;JAIN, SILPI
    • Kyungpook Mathematical Journal
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    • 제55권3호
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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.

TURÁN-TYPE INEQUALITIES FOR GAUSS AND CONFLUENT HYPERGEOMETRIC FUNCTIONS VIA CAUCHY-BUNYAKOVSKY-SCHWARZ INEQUALITY

  • Bhandari, Piyush Kumar;Bissu, Sushil Kumar
    • 대한수학회논문집
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    • 제33권4호
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    • pp.1285-1301
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    • 2018
  • This paper is devoted to the study of $Tur{\acute{a}}n$-type inequalities for some well-known special functions such as Gauss hypergeometric functions, generalized complete elliptic integrals and confluent hypergeometric functions which are derived by using a new form of the Cauchy-Bunyakovsky-Schwarz inequality. We also apply these inequalities for some sample of interest such as incomplete beta function, incomplete gamma function, elliptic integrals and modified Bessel functions to obtain their corresponding $Tur{\acute{a}}n$-type inequalities.

DECOMPOSITION FORMULAS AND INTEGRAL REPRESENTATIONS FOR SOME EXTON HYPERGEOMETRIC FUNCTIONS

  • Choi, Junesang;Hasanov, Anvar;Turaev, Mamasali
    • 충청수학회지
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    • 제24권4호
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    • pp.745-758
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    • 2011
  • Generalizing the Burchnall-Chaundy operator method, the authors are aiming at presenting certain decomposition formulas for the chosen six Exton functions expressed in terms of Appell's functions $F_3$ and $F_4$, Horn's functions $H_3$ and $H_4$, and Gauss's hypergeometric function F. We also give some integral representations for the Exton functions $X_i$ (i = 6, 8, 14) each of whose kernels contains the Horn's function $H_4$.

INTEGRAL REPRESENTATIONS FOR SRIVASTAVA'S HYPERGEOMETRIC FUNCTION HA

  • Choi, June-Sang;Hasanov, Anvar;Turaev, Mamasali
    • 호남수학학술지
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    • 제34권1호
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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
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제19권2호
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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 $H_B$.

INTEGRAL REPRESENTATIONS FOR SRIVASTAVA'S HYPERGEOMETRIC FUNCTION HC

  • Choi, Junesang;Hasanov, Anvar;Turaev, Mamasali
    • 호남수학학술지
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    • 제34권4호
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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 $H_C$.

SOME APPLICATIONS FOR GENERALIZED FRACTIONAL OPERATORS IN ANALYTIC FUNCTIONS SPACES

  • Kilicman, Adem;Abdulnaby, Zainab E.
    • Korean Journal of Mathematics
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    • 제27권3호
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    • pp.581-594
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    • 2019
  • In this study a new generalization for operators of two parameters type of fractional in the unit disk is proposed. The fractional operators in this generalization are in the Srivastava-Owa sense. Concerning with the related applications, the generalized Gauss hypergeometric function is introduced. Further, some boundedness properties on Bloch space are also discussed.

EXTENDED HYPERGEOMETRIC FUNCTIONS OF TWO AND THREE VARIABLES

  • AGARWAL, PRAVEEN;CHOI, JUNESANG;JAIN, SHILPI
    • 대한수학회논문집
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    • 제30권4호
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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.

CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X8

  • Choi, June-Sang;Hasanov, Anvar;Turaev, Mamasali
    • 대한수학회논문집
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    • 제27권2호
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    • pp.257-264
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    • 2012
  • Exton introduced 20 distinct triple hypergeometric functions whose names are $X_i$ (i = 1, ${\ldots}$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function ${\Psi}_1$, and a Humbert function ${\Phi}_2$. The object of this paper is to present 18 new integral representations of Euler type for the Exton hypergeometric function $X_8$, whose kernels include the Exton functions ($X_2$, $X_8$) itself, the Horn's function $H_4$, the Gauss hypergeometric function $F$, and Lauricella hypergeometric function $F_C$. We also provide a system of partial differential equations satisfied by $X_8$.