• Title, Summary, Keyword: basic hypergeometric series

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THREE-TERM CONTIGUOUS FUNCTIONAL RELATIONS FOR BASIC HYPERGEOMETRIC SERIES 2φ1

  • KIM, YONG-SUP;RATHIE ARJUN K.;CHOI, JUNE-SANG
    • Communications of the Korean Mathematical Society
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    • v.20 no.2
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    • pp.395-403
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    • 2005
  • The authors aim mainly at giving fifteen three-term contiguous relations for the basic hypergeometric series $series\;_2{\phi}_1$ corresponding to Gauss's contiguous relations for the hypergeometric series $series\;_2F_1$ given in Rainville([6], p.71). They also apply them to obtain two summation formulas closely related to a known q-analogue of Kummer's theorem.

CERTAIN NEW WP-BAILEY PAIRS AND BASIC HYPERGEOMETRIC SERIES IDENTITIES

  • Ali, S. Ahmad;Rizvi, Sayyad Nadeem Hasan
    • Communications of the Korean Mathematical Society
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    • v.32 no.4
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    • pp.885-898
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    • 2017
  • The Bailey lemma has been a powerful tool in the discovery of identities of Rogers-Ramanujan type and also ordinary and basic hyper-geometric series identities. The mechanism of Bailey lemma has also led to the concepts of Bailey pair and Bailey chain. In the present work certain new WP-Bailey pairs have been established. We also have deduced a number of basic hypergeometric series identities as an application of new WP-Bailey pairs.

RECURSION FORMULAS FOR q-HYPERGEOMETRIC AND q-APPELL SERIES

  • Sahai, Vivek;Verma, Ashish
    • Communications of the Korean Mathematical Society
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    • v.33 no.1
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    • pp.207-236
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    • 2018
  • 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.

ON THE BERGMAN KERNEL FOR SOME HARTOGS DOMAINS

  • Park, Jong-Do
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.2
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    • pp.521-533
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    • 2020
  • In this paper, we compute the Bergman kernel for Ωp,q,r = {(z, z', w) ∈ ℂ2 × Δ : |z|2p < (1 - |z'|2q)(1 - |w|2)r}, where p, q, r > 0 in terms of multivariable hypergeometric series. As a consequence, we obtain the behavior of KΩp,q,r (z, 0, 0; z, 0, 0) when (z, 0, 0) approaches to the boundary of Ωp,q,r.

Confluent Hypergeometric Distribution and Its Applications on Certain Classes of Univalent Functions of Conic Regions

  • Porwal, Saurabh
    • Kyungpook Mathematical Journal
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    • v.58 no.3
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    • pp.495-505
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    • 2018
  • The purpose of the present paper is to investigate Confluent hypergeometric distribution. We obtain some basic properties of this distribution. It is worthy to note that the Poisson distribution is a particular case of this distribution. Finally, we give a nice application of this distribution on certain classes of univalent functions of the conic regions.

ON MATRIX POLYNOMIALS ASSOCIATED WITH HUMBERT POLYNOMIALS

  • Pathan, M.A.;Bin-Saad, Maged G.;Al-Sarahi, Fadhl
    • The Pure and Applied Mathematics
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    • v.21 no.3
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    • pp.207-218
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    • 2014
  • The principal object of this paper is to study a class of matrix polynomials associated with Humbert polynomials. These polynomials generalize the well known class of Gegenbauer, Legendre, Pincherl, Horadam, Horadam-Pethe and Kinney polynomials. We shall give some basic relations involving the Humbert matrix polynomials and then take up several generating functions, hypergeometric representations and expansions in series of matrix polynomials.

MOCK THETA FUNCTIONS OF ORDER 2 AND THEIR SHADOW COMPUTATIONS

  • Kang, Soon-Yi;Swisher, Holly
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.6
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    • pp.2155-2163
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    • 2017
  • Zwegers showed that a mock theta function can be completed to form essentially a real analytic modular form of weight 1/2 by adding a period integral of a certain weight 3/2 unary theta series. This theta series is related to the holomorphic modular form called the shadow of the mock theta function. In this paper, we discuss the computation of shadows of the second order mock theta functions and show that they share the same shadow with a mock theta function which appears in the Mathieu moonshine phenomenon.