• Title/Summary/Keyword: inverse pairs of symbolic operators

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DECOMPOSITION FORMULAS FOR THE GENERALIZID HYPERGEOMETRIC 4F3 FUNCTION

  • Hasanov, Anvar;Turaev, Mamasali;Choi, June-Sang
    • Honam Mathematical Journal
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    • v.32 no.1
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    • pp.1-16
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    • 2010
  • By using the generalized operator method given by Burchnall and Chaundy in 1940, the authors present one-dimensional inverse pairs of symbolic operators. Many operator identities involving these pairs of symbolic operators are rst constructed. By means of these operator identities, 11 decomposition formulas for the generalized hypergeometric $_4F_3$ function are then given. Furthermore, the integral representations associated with generalized hypergeometric functions are also presented.

SOME DECOMPOSITION FORMULAS ASSOCIATED WITH THE SARAN FUNCTION FE

  • Kim, Yong-Sup;Hasanov, Anvar;Lee, Chang-Hyun
    • Honam Mathematical Journal
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    • v.32 no.4
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    • pp.581-592
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    • 2010
  • With the help of some techniques based upon certain inverse pairs of symbolic operators initiated by Burchnall-Chaundy, the authors investigate decomposition formulas associated with Saran's function $F_E$ in three variables. Many operator identities involving these pairs of symbolic operators are first constructed for this purpose. By employing their decomposition formulas, we also present a new group of integral representations for the Saran function $F_E$.

DECOMPOSITION FORMULAS AND INTEGRAL REPRESENTATIONS FOR SOME EXTON HYPERGEOMETRIC FUNCTIONS

  • Choi, Junesang;Hasanov, Anvar;Turaev, Mamasali
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.4
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    • pp.745-758
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    • 2011
  • Generalizing the Burchnall-Chaundy operator method, the authors are aiming at presenting certain decomposition formulas for the chosen six Exton functions expressed in terms of Appell's functions $F_3$ and $F_4$, Horn's functions $H_3$ and $H_4$, and Gauss's hypergeometric function F. We also give some integral representations for the Exton functions $X_i$ (i = 6, 8, 14) each of whose kernels contains the Horn's function $H_4$.

DECOMPOSITION FORMULAS AND INTEGRAL REPRESENTATIONS FOR THE KAMPÉ DE FÉRIET FUNCTION F0:3;32:0;0 [x, y]

  • Choi, Junesang;Turaev, Mamasali
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.4
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    • pp.679-689
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    • 2010
  • By developing and using certain operators like those initiated by Burchnall-Chaundy, the authors aim at investigating several decomposition formulas associated with the $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ function $F_{2:0;0}^{0:3;3}$ [x, y]. For this purpose, many operator identities involving inverse pairs of symbolic operators are constructed. By employing their decomposition formulas, they also present a new group of integral representations of Eulerian type for the $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ function $F_{2:0;0}^{0:3;3}$ [x, y], some of which include several hypergeometric functions such as $_2F_1$, $_3F_2$, an Appell function $F_3$, and the $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ functions $F_{2:0;0}^{0:3;3}$ and $F_{1:0;1}^{0:2;3}$.

FRACTIONAL DIFFERENTIATIONS AND INTEGRATIONS OF QUADRUPLE HYPERGEOMETRIC SERIES

  • Bin-Saad, Maged G.;Nisar, Kottakkaran S.;Younis, Jihad A.
    • Communications of the Korean Mathematical Society
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    • v.36 no.3
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    • pp.495-513
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    • 2021
  • The hypergeometric series of four variables are introduced and studied by Bin-Saad and Younis recently. In this line, we derive several fractional derivative formulas, integral representations and operational formulas for new quadruple hypergeometric series.

APPLICATION OF THE OPERATOR H (α, β) TO THE SARAN FUNCTION FE AND SOME OTHER RESULTS

  • Choi, June-Sang;Kim, Yong-Sup;Hasanov, Anvar
    • Honam Mathematical Journal
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    • v.33 no.4
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    • pp.441-452
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    • 2011
  • The enormous success of the theory of hypergeometric series in a single variable has stimulated the development of a corresponding theory in two and more variables. A wide variety of investigations in the theory of several variable hypergeometric functions have been essentially motivated by the fact that solutions of many applied problems involving partial differential equations are obtainable with the help of such hypergeometric functions. Here, in this trend, we aim at presenting further decomposition formulas for Saran function $F_E$, which are used to give some integral representations of the function $F_E$. We also present a system of partial differential equations for the Saran function $F_E$.