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Recursion Formulas for $q$-hypergeometric and $q$-Appell series

Vivek Sahai|Ashish Verma
대한수학회 (The Korean Mathematical Society)|2018.01|대한수학회논문집 (Communications of the KMS)|제33권 제1호|pp. 207-236

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키워드

recursion formulasgeneralized basic hypergeometric series$q$-Appell seriesgeneral double $q$-hypergeometric series
주제분류수학

초록

We obtain recursion formulas for $q$-hypergeometric and $q$-Appell series. We also find recursion formulas for the general double $q$-hypergeometric series. It is shown that these recursion relations can be expressed in terms of $q$-derivatives of the respective $q$-hypergeometric series.

Abstract

We obtain recursion formulas for $q$-hypergeometric and $q$-Appell series. We also find recursion formulas for the general double $q$-hypergeometric series. It is shown that these recursion relations can be expressed in terms of $q$-derivatives of the respective $q$-hypergeometric series.

참고문헌 (12)

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  2. F. H. Jackson, "On basic double hypergeometric functions", Quart. J. Math. (Oxford), 13, pp.69~82 (1942)
  3. S. B. Opps, "Recursion formulas for Appell's hyperge-ometric function <TEX>$F_2$<", TEX> with some applications to radiation field problems, 2009, pp.207(2), 545~558
  4. E. D. Rainville, "Special Functions" (1960), Chelsea Publishing Company
  5. V. Sahai, "Recursion formulas for multivariable hypergeometric functions", Asian-Eur. J. Math., 8(4), pp.50~ (2015)
  6. Vivek Sahai, "Recursion Formulas for Exton's triple Hypergeometric Functions", Kyungpook Mathematical Journal, 56(2), pp.473~506 (2016), 경북대학교 자연과학대학 수학과
  7. V. Sahai, "Recursion formulas for Srivastava's general triple hypergeometric function", Asian-Eur. J. Math., 9(3), pp.1650063~1650079 (2016)[DOI]
  8. V. Sahai, "Recursion formulas for the Srivastava-Daoust and related multivariable hyper-geometric functions", Asian-Eur. J. Math., 9(4), pp.1650081~1650115 (2016)[DOI]
  9. H. M. Srivastava, "Certain generalized Neumann expansions associated with the Kampe de Feriet function", Indag. Math., 31, pp.449~457 (1969)
  10. 1985, , ~
  11. R. F. Swarttouw, "The contiguous function relations for basic hypergeometric function", J. Math. Anal. Appl., 149(1), pp.151~159 (1990)[DOI]
  12. X. Wang, "Recursion formulas for Appell functions", Integral Transforms Spec. Funct., 23(6), pp.421~433 (2012)[DOI]

관련 논문AI추천

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