• 제목/요약/키워드: Kamp$\acute{e}$ de F$\acute{e}$riet series

검색결과 11건 처리시간 0.028초

FUNCTIONAL RELATIONS INVOLVING SRIVASTAVA'S HYPERGEOMETRIC FUNCTIONS HB AND F(3)

  • Choi, Junesang;Hasanov, Anvar;Turaev, Mamasali
    • 충청수학회지
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    • 제24권2호
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    • pp.187-204
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    • 2011
  • B. C. Carlson [Some extensions of Lardner's relations between $_0F_3$ and Bessel functions, SIAM J. Math. Anal. 1(2) (1970), 232-242] presented several useful relations between Bessel and generalized hypergeometric functions that generalize some earlier results. Here, by simply splitting Srivastava's hypergeometric function $H_B$ into eight parts, we show how some useful and generalized relations between Srivastava's hypergeometric functions $H_B$ and $F^{(3)}$ can be obtained. These main results are shown to be specialized to yield certain relations between functions $_0F_1$, $_1F_1$, $_0F_3$, ${\Psi}_2$, and their products including different combinations with different values of parameters and signs of variables. We also consider some other interesting relations between the Humbert ${\Psi}_2$ function and $Kamp\acute{e}$ de $F\acute{e}riet$ function, and between the product of exponential and Bessel functions with $Kamp\acute{e}$ de $F\acute{e}riet$ functions.

ON THE REDUCIBILITY OF KAMPÉ DE FÉRIET FUNCTION

  • Choi, Junesang;Rathie, Arjun K.
    • 호남수학학술지
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    • 제36권2호
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    • pp.345-355
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    • 2014
  • The main objective of this paper is to obtain a formula containing eleven interesting results for the reducibility of Kamp$\acute{e}$ de F$\acute{e}$riet function. The results are derived with the help of two general results for the series $_2F_1(2)$ very recently presented by Kim et al. Well known Kummer's second theorem and its contiguous results proved earlier by Rathie and Nagar, and Kim et al. follow special cases of our main findings.

ON AN EXTENSION FORMULAS FOR THE TRIPLE HYPERGEOMETRIC SERIES X8 DUE TO EXTON

  • Kim, Yong-Sup;Rathie, Arjun K.
    • 대한수학회보
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    • 제44권4호
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    • pp.743-751
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    • 2007
  • The aim of this article is to derive twenty five transformation formulas in the form of a single result for the triple hypergeometric series $X_8$ introduced earlier by Exton. The results are derived with the help of generalized Watson#s theorem obtained earlier by Lavoie et al. An interesting special cases are also pointed out.

Reduction Formulas for Srivastava's Triple Hypergeometric Series F(3)[x, y, z]

  • CHOI, JUNESANG;WANG, XIAOXIA;RATHIE, ARJUN K.
    • Kyungpook Mathematical Journal
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    • 제55권2호
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    • pp.439-447
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    • 2015
  • Very recently the authors have obtained a very interesting reduction formula for the Srivastava's triple hypergeometric series $F^{(3)}$(x, y, z) by applying the so-called Beta integral method to the Henrici's triple product formula for the hypergeometric series. In this sequel, we also present three more interesting reduction formulas for the function $F^{(3)}$(x, y, z) by using the well known identities due to Bailey and Ramanujan. The results established here are simple, easily derived and (potentially) useful.

GENERALIZATION OF WHIPPLE'S THEOREM FOR DOUBLE SERIES

  • RATHIE, ARJUN K.;GAUR, VIMAL K.;KIM, YONG SUP;PARK, CHAN BONG
    • 호남수학학술지
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    • 제26권1호
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    • pp.119-132
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    • 2004
  • In 1965, Bhatt and Pandey have obtained an analogue of the Whipple's theorem for double series by using Watson's theorem on the sum of a $_3F_2$. The aim of this paper is to derive twenty five results for double series closely related to the analogue of the Whipple's theorem for double series obtained by Bhatt and Pandey. The results are derived with the help of twenty five summation formulas closely related to the Watson's theorem on the sum of a $_3F_2$ obtained recently by Lavoie, Grondin, and Rathie.

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

  • Kim, Yong-Sup;Choi, June-Sang;Rathie, Arjun K.
    • 대한수학회보
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    • 제49권3호
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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.

ON DOUBLE INFINITE SERIES INVOLVING THE H-FUNCTION OF TWO VARIABLES

  • Handa, S.
    • Kyungpook Mathematical Journal
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    • 제18권2호
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    • pp.257-262
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    • 1978
  • In this paper, we obtain two new double infinite series for the H-function of two variables, by which we also obtain a single infinite series involving the H-function of two variable3. On account of the most general nature of the H-functin of two variables, a number of related double infinite series for simpler functions follow as special cases of our results. As an illustration, we obtain here from one of our main series, the corresponding series for $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ function and Fox's H-function. A number of other series involving a very large, spectrum of special functions also follow as special cases of our main series but, we are not recording them here for want of space.

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Serendipitous Functional Relations Deducible from Certain Generalized Triple Hypergeometric Functions

  • Choi, June-Sang;Hasanov, Anvar;Turaev, Mamasali
    • Kyungpook Mathematical Journal
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    • 제52권2호
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    • pp.109-136
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    • 2012
  • We aim at presenting certain unexpected functional relations among various hypergeometric functions of one or several variables (for example, see the identities in Corollary 5) by making use of Carlson's method employed in his work (Some extensions of Lardner's relations between $_0F_3$ and Bessel functions, SIAM J. Math. Anal. 1(2)(1970), 232-242).