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Decomposition formulae for generalized hypergeometric functions with the Gauss-Kummer identity

Naoya HAYASHI|Yutaka MATSUI
대한수학회 (The Korean Mathematical Society)|2014.01|대한수학회논문집 (Communications of the KMS)|제29권 제1호|pp. 97-108

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참고문헌

키워드

generalized hypergeometric functionsGauss-Kummer identitydecomposition formulae
주제분류수학

초록

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.

Abstract

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.

참고문헌 (11)

  1. J. L. Burchnall, "Expansions of Appell's double hypergeometric functions", Quart. J. Math. Oxford Ser, 11, pp.249~270 (1940)
  2. J. L. Burchnall, "Expansions of Appell's double hypergeometric function. II", Quart. J. Math. Oxford Ser, 12, pp.112~128 (1941)
  3. T. W. Chaundy, "Expansions of hypergeometric functions", Quart. J. Math. Oxford Ser, 13, pp.159~171 (1942)
  4. J. Choi, "Applications of the operator H(α, β) to the Humbert double hypergeometric functions", Comput. Math. Appl, 61(3), pp.663~671 (2011)
  5. 최준상, "CERTAIN DECOMPOSITION FORMULAS OF GENERALIZED HYPERGEOMETRIC FUNCTIONS pFq AND SOME FORMULAS OF AN ANALYTIC CONTINUATION OF THE CLAUSEN FUNCTION ₃F₂", 대한수학회논문집, 27(1), pp.107~116 (2012), 대한수학회
  6. A. Hasanov, "Some decomposition formulas associated with the Lauricella function FA(γ) and other multiple hypergeometric functions", Appl. Math. Lett, 19(2), pp.113~121 (2006)
  7. A. Hasanov, "Decomposition formulas associated with the Lauricella multivariable hypergeometric functions", Compt. Math. Appl, 53(7), pp.1119~1128 (2007)
  8. A. Hasanov, "Decomposition formulas for some triple hypergeometric functions", J. Math. Anal. Appl, 324(2), pp.955~969 (2006)
  9. Anvar Hasanov, "DECOMPOSITION FORMULAS FOR THE GENERALIZID HYPERGEOMETRIC 4F3 FUNCTION", 호남수학학술지, 32(1), pp.1~16 (2010), 호남수학회
  10. K. Iwasaki, "From Gauss to Painleve, A modern theory of special functions" (1991), Friedr. Vieveg & Sohn, Braunschweig
  11. H. M. Srivastava, "Multiple Gaussian Hypergeometric Series" (1985), Halsted press

관련 논문AI추천

CERTAIN DECOMPOSITION FORMULAS OF GENERALIZED HYPERGEOMETRIC FUNCTIONS pFq AND SOME FORMULAS OF AN ANALYTIC CONTINUATION OF THE CLAUSEN FUNCTION ₃F₂최준상, Anvar Hasanov대한수학회 · 대한수학회논문집2012 · 제27권 제1호Certain reduction and transformation formulas for the Kamp\'{e} de F\'{e}riet functionArjun K. Rathie, Medhat A. Rakha대한수학회 · 대한수학회논문집2022 · 제37권 제2호GENERALIZATIONS OF TWO SUMMATION FORMULAS FOR THE GENERALIZED HYPERGEOMETRIC FUNCTION OF HIGHER ORDER DUE TO EXTON최준상, Arjun Kumar Rathie대한수학회 · 대한수학회논문집2010 · 제25권 제3호Two general hypergeometric transformation formulas최준상, Arjun K. Rathie대한수학회 · 대한수학회논문집2014 · 제29권 제4호Generalized Incomplete Pochhammer Symbols and Their Applications to Hypergeometric functionsAshish Verma, Vivek Sahai경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2018 · 제58권 제1호Generating functions for the extended Wright type hypergeometric functionAjay Kumar Shukla, Bhumika Maheshwari, Ranjan Kumar Jana대한수학회 · 대한수학회논문집2017 · 제32권 제1호

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