• 제목/요약/키워드: Mellin-Barnes contour integral

검색결과 5건 처리시간 0.021초

CERTAIN CLASSES OF INFINITE SERIES DEDUCIBLE FROM MELLIN-BARNES TYPE OF CONTOUR INTEGRALS

  • Choi, Junesang;Agarwal, Praveen
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제20권4호
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    • pp.233-242
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    • 2013
  • Certain interesting single (or double) infinite series associated with hypergeometric functions have been expressed in terms of Psi (or Digamma) function ${\psi}(z)$, for example, see Nishimoto and Srivastava [8], Srivastava and Nishimoto [13], Saxena [10], and Chen and Srivastava [5], and so on. In this sequel, with a view to unifying and extending those earlier results, we first establish two relations which some double infinite series involving hypergeometric functions are expressed in a single infinite series involving ${\psi}(z)$. With the help of those series relations we derived, we next present two functional relations which some double infinite series involving $\bar{H}$-functions, which are defined by a generalized Mellin-Barnes type of contour integral, are expressed in a single infinite series involving ${\psi}(z)$. The results obtained here are of general character and only two of their special cases, among numerous ones, are pointed out to reduce to some known results.

AN EXTENSION OF THE EXTENDED HURWITZ-LERCH ZETA FUNCTIONS OF TWO VARIABLES

  • Choi, Junesang;Parmar, Rakesh K.;Saxena, Ram K.
    • 대한수학회보
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    • 제54권6호
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    • pp.1951-1967
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    • 2017
  • We aim to introduce a further extension of a family of the extended Hurwitz-Lerch Zeta functions of two variables. We then systematically investigate several interesting properties of the extended function such as its integral representations which provide extensions of various earlier corresponding results of two and one variables, its summation formula, its Mellin-Barnes type contour integral representations, its computational representation and fractional derivative formulas. A multi-parameter extension of the extended Hurwitz-Lerch Zeta function of two variables is also introduced. Relevant connections of certain special cases of the main results presented here with some known identities are pointed out.

ON AN INTEGRAL INVOLVING Ī-FUNCTION

  • D'Souza, Vilma;Kurumujji, Shantha Kumari
    • 대한수학회논문집
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    • 제37권1호
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    • pp.207-212
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    • 2022
  • In this paper, an interesting integral involving the Ī-function of one variable introduced by Rathie has been derived. Since Ī-function is a very generalized function of one variable and includes as special cases many of the known functions appearing in the literature, a number of integrals can be obtained by reducing the Ī function of one variable to simpler special functions by suitably specializing the parameters. A few special cases of our main results are also discussed.

CERTAIN INTEGRALS INVOLVING THE PRODUCT OF GAUSSIAN HYPERGEOMETRIC FUNCTION AND ALEPH FUNCTION

  • Suthar, D.L.;Agarwal, S.;Kumar, Dinesh
    • 호남수학학술지
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    • 제41권1호
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    • pp.1-17
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    • 2019
  • The aim of this paper is to establish certain integrals involving product of the Aleph function with exponential function and multi Gauss's hypergeometric function. Being unified and general in nature, these integrals yield a number of known and new results as special cases. For the sake of illustration, twelve corollaries are also recorded here as special case of our main results.

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

  • Choi, Junesang;Turaev, Mamasali
    • 충청수학회지
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    • 제23권4호
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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 $F_{1:0;1}^{0:2;3}$.