본문 바로가기
KERD
논문KCI 등재

Some integral representations and transforms for extended generalized Appell's and Lauricella's hypergeometric functions

김용섭
대한수학회 (The Korean Mathematical Society)|2017.04|대한수학회논문집 (Communications of the KMS)|제32권 제2호|pp. 321-332

1

조회

0

다운로드

1

인용

0

참고문헌

키워드

Mellin transformbeta functionAppell functionsLauricella's hypergeometric functions
주제분류수학

초록

In this paper, we generalize the extended Appell's and Lauricella's hypergeometric functions which have recently been introduced by Liu \cite{LIU} and Khan \cite{KG}. Also, we aim at establishing some (presumbly) new integral representations and transforms for the extended generalized Appell's and Lauricella's hypergeometric functions.

Abstract

In this paper, we generalize the extended Appell's and Lauricella's hypergeometric functions which have recently been introduced by Liu \cite{LIU} and Khan \cite{KG}. Also, we aim at establishing some (presumbly) new integral representations and transforms for the extended generalized Appell's and Lauricella's hypergeometric functions.

참고문헌 (18)

  1. Praveen Agarwal, "Extended hypergeometric functions of two and three variables", 대한수학회논문집, 30(4), pp.403~414 (2015), 대한수학회
  2. G. E. Andrews, "Special Functions" (1999), Cambridge University Press
  3. M. A. Chaudhry, "Extension of Euler’s beta function", J. Comput. Appl. Math, 78(1), pp.19~32 (1997)
  4. M. A. Chaudhry, "Extended hypergeometric and confluent hypergeometric function", Appl. Math. Comput, 159(2), pp.589~602 (2004)
  5. A. Hasanov, "Some decomposition formulas associated with the Lauricella function F (r)A and other multiple hypergeometric functions", Appl. Math. Comput, 187, pp.195~201 (2007)
  6. A. Hasanov, "Decomposition formulas associated with the Lauricella multivariable hypergeo-metric functions", Comput. Math. Appl, 53(7), pp.1119~1128 (2007)
  7. N. U. Khan, "Generalization of extended Appell's and Lauricella's hypergeometric functions", 호남수학학술지, 37(1), pp.113~126 (2015), 호남수학회
  8. 이동명, "GENERALIZATION OF EXTENDED BETA FUNCTION, HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTIONS", 호남수학학술지, 33(2), pp.187~206 (2011), 호남수학회
  9. H. Liu, "Some generating relations for extended Appell’s and Lauricella hypergeometric functions", Rocky Moutain J. Math, 41(6), pp.1987~2007 (2014)
  10. M. J. Luo, "Some results on the extended beta and extended hypergeometric functions", Appl. Math. Comput, 248, pp.631~651 (2014)
  11. M. A. ¨Ozarslan, "Some generating relations for extended hypergeometric functions via generalized fractional derivative operator", Math. Comp. Model, 52(9-10), pp.1825~1833 (2010)
  12. E. ¨Ozergin, "Extension of gamma, beta and hypergeometric functions", J. Comput. Appl. Math, 235(16), pp.4601~4610 (2011)
  13. E. D. Rainville, "Special Functions" (1960), Macmillan
  14. H. M. Srivastava, "Generating functions for the generalized Gauss hypergeometric functions", Appl. Math. Comput, 247, pp.348~352 (2014)
  15. H. M. Srivastava, "Zeta and q-Zeta Functions and Associated Series and Integrals" (2012), Elsvier Science Publishers
  16. H.M. Srivastava, "A Treatise on Generating Functions" (1984), Ellis Horwood Limited
  17. R. Vid˜unas, "Specialization of Appell’s functions to univariate hypergeometric functions", J. Math. Anal. Appl, 355(1), pp.145~163 (2009)
  18. "Hypergeometric 1F1"[URL]

관련 논문AI추천

Extended Lauricella and Appell Functions and Their Associated PropertiesH. M. Srivastava, M. M. Joshi, R. K. Parmar장전수학회 · Advanced Studies in Contemporary Mathematics2015 · 제25권 제2호Some integral transforms and fractional integral formulas for the extended hypergeometric functions최준상, Hui Zhou, Jyotindra C. Prajapati, Krunal B. Kachhia, Praveen Agarwal대한수학회 · 대한수학회논문집2016 · 제31권 제3호Some $\tau$-extensions of Lauricella functions of several variablesRakesh Kumar Parmar, Shyam Lal Kalla, Sunil Dutt Purohit대한수학회 · 대한수학회논문집2015 · 제30권 제3호The Incomplete Lauricella Functions of Several Variables and Associated Properties and Formulas최준상, H. M. Srivastava, Rakesh K. Parmar경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2018 · 제58권 제1호Extended hypergeometric functions of two and three variables최준상, Praveen Agarwal, Shilpi Jain대한수학회 · 대한수학회논문집2015 · 제30권 제4호EXTENSIONS OF MULTIPLE LAURICELLA AND HUMBERT’S CONFLUENT HYPERGEOMETRIC FUNCTIONS THROUGH A HIGHLY GENERALIZED POCHHAMMER SYMBOL AND THEIR RELATED PROPERTIES최준상, Naveen Kumar, Rakesh K. Parmar, RITU AGARWAL대한수학회 · 대한수학회보2023 · 제60권 제3호

이 간행물의 다른 논문 (19건)

On the divisor-class group of monadic submonoids of rings of integer-valued polynomialsAndreas Reinhartpp. 233-260A note on Jordan derivations of trivial generalized matrix algebrasChenyou Zheng, Yanbo Lipp. 261-266Rings with many regular elementsEbrahim Nasibi, Nahid Ashrafipp. 267-276On subdirect product of prime modulesNajmeh Dehghani, Mohammad Reza Vedadipp. 277-285Incomplete extended Hurwitz-Lerch zeta functions and associated propertiesRam K. Saxena, Rakesh K. Parmarpp. 287-304
원문 보기