• Title/Summary/Keyword: Kummer-type transformation

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

  • Choi, June-Sang;Rathie, Arjun K.
    • Communications of the Korean Mathematical Society
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    • v.22 no.3
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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.

An Identity Involving Product of Generalized Hypergeometric Series 2F2

  • Kim, Yong Sup;Choi, Junesang;Rathie, Arjun Kumar
    • Kyungpook Mathematical Journal
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    • v.59 no.2
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    • pp.293-299
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    • 2019
  • A number of identities associated with the product of generalized hypergeometric series have been investigated. In this paper, we aim to establish an identity involving the product of the generalized hypergeometric series $_2F_2$. We do this using the generalized Kummer-type II transformation due to Rathie and Pogany and another identity due to Bailey. The result presented here, being general, can be reduced to a number of relatively simple identities involving the product of generalized hypergeometric series, some of which are observed to correspond to known ones.

TWO RESULTS FOR THE TERMINATING 3F2(2) WITH APPLICATIONS

  • Kim, Yong-Sup;Choi, June-Sang;Rathie, Arjun K.
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.3
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    • pp.621-633
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    • 2012
  • By establishing a new summation formula for the series $_3F_2(\frac{1}{2})$, recently Rathie and Pogany have obtained an interesting result known as Kummer type II transformation for the generalized hypergeometric function $_2F_2$. Here we aim at deriving their result by using a very elementary method and presenting two elegant results for certain terminating series $_3F_2(2)$. Furthermore two interesting applications of our new results are demonstrated.