• 제목/요약/키워드: Kummer's theorem

검색결과 31건 처리시간 0.027초

ON BASIC ANALOGUE OF CLASSICAL SUMMATION THEOREMS DUE TO ANDREWS

  • Harsh, Harsh Vardhan;Rathie, Arjun K.;Purohit, Sunil Dutt
    • 호남수학학술지
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    • 제38권1호
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    • pp.25-37
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    • 2016
  • In 1972, Andrews derived the basic analogue of Gauss's second summation theorem and Bailey's theorem by implementing basic analogue of Kummer's theorem into identity due to Jackson. Recently Lavoie et.al. derived many results closely related to Kummer's theorem, Gauss's second summation theorem and Bailey's theorem and also Rakha et. al. derive the basic analogues of results closely related Kummer's theorem. The aim of this paper is to derive basic analogues of results closely related Gauss's second summation theorem and Bailey's theorem. Some applications and limiting cases are also considered.

APPLICATIONS OF GENERALIZED KUMMER'S SUMMATION THEOREM FOR THE SERIES 2F1

  • Kim, Yong-Sup;Rathie, Arjun K.
    • 대한수학회보
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    • 제46권6호
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    • pp.1201-1211
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    • 2009
  • The aim of this research paper is to establish generalizations of classical Dixon's theorem for the series $_3F_2$, a result due to Bailey involving product of generalized hypergeometric series and certain very interesting summations due to Ramanujan. The results are derived with the help of generalized Kummer's summation theorem for the series $_2F_1$ obtained earlier by Lavoie, Grondin, and Rathie.

ANOTHER PROOF OF KUMMER'S SECOND THEOREM

  • Arjun K. Rathie;Choi, June-Sang
    • 대한수학회논문집
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    • 제13권4호
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    • pp.933-936
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    • 1998
  • We aim at giving another method of proving the well-known and useful Kummer's second theorem without changing its original form.

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OTHER PROOFS OF KUMMER'S SECOND THEOREM

  • Malani, Shaloo;Choi, June-Sang
    • East Asian mathematical journal
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    • 제17권1호
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    • pp.129-133
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    • 2001
  • The aim of this research note is to derive the well known Kummer's second theorem by transforming the integrals which represent some generalized hypergeometric functions. This theorem can also be shown by combining two known Bailey's and Preece's identities for the product of generalized hypergeometric series.

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ANOTHER METHOD FOR A KUMMER-TYPE TRANSFORMATION FOR A 2F2 HYPERGEOMETRIC FUNCTION

  • Choi, June-Sang;Rathie, Arjun K.
    • 대한수학회논문집
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    • 제22권3호
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    • pp.369-371
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    • 2007
  • Very recently, by employing an addition theorem for the con-fluent hypergeometric function, Paris has obtained a Kummer-type trans-formation for a $_2F_2(x)$ hypergeometric function with general parameters in the form of a sum of $_2F_2(-x)$ functions. The aim of this note is to derive his result without using the addition theorem.

ALTERNATIVE DERIVATIONS OF CERTAIN SUMMATION FORMULAS CONTIGUOUS TO DIXON'S SUMMATION THEOREM FOR A HYPERGEOMETRIC $_3F_2$ SERIES

  • Choi, June-Sang;Rathie Arjun K.;Malani Shaloo;Mathur Rachana
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제13권4호
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    • pp.255-259
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    • 2006
  • In 1994, Lavoie et al. have obtained twenty tree interesting results closely related to the classical Dixon's theorem on the sum of a $_3F_2$ by making a systematic use of some known relations among contiguous functions. We aim at showing that these results can be derived by using the same technique developed by Bailey with the help of Gauss's summation theorem and generalized Kummer's theorem obtained by Lavoie et al..

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AN EXTENSION OF THE TRIPLE HYPERGEOMETRIC SERIES BY EXTON

  • Lee, Seung-Woo;Kim, Yong-Sup
    • 호남수학학술지
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    • 제32권1호
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    • pp.61-71
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    • 2010
  • The aim of this paper is to extend a number of transformation formulas for the four $X_4$, $X_5$, $X_7$, and $X_8$ among twenty triple hypergeometric series $X_1$ to $X_{20}$ introduced earlier by Exton. The results are derived from the generalized Kummer's theorem and Dixon's theorem obtained earlier by Lavoie et al..