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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.20 No.4

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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2013, v.20 no.4, pp.233-242
https://doi.org/10.7468/jksmeb.2013.20.4.233
Choi, Junesang
Agarwal, Praveen
Choi,, J. , & Agarwal,, P. (2013). CERTAIN CLASSES OF INFINITE SERIES DEDUCIBLE FROM MELLIN-BARNES TYPE OF CONTOUR INTEGRALS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 20(4), 233-242, https://doi.org/10.7468/jksmeb.2013.20.4.233

Abstract

Certain interesting single (or double) infinite series associated with hypergeometric functions have been expressed in terms of Psi (or Digamma) function <TEX>${\psi}(z)$</TEX>, 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 <TEX>${\psi}(z)$</TEX>. With the help of those series relations we derived, we next present two functional relations which some double infinite series involving <TEX>$\bar{H}$</TEX>-functions, which are defined by a generalized Mellin-Barnes type of contour integral, are expressed in a single infinite series involving <TEX>${\psi}(z)$</TEX>. 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.

keywords
gamma function, Pochhammer symbol, Psi (or Digamma) function, generalized hypergeometric function <tex> $_pF_q$</tex>, H-function, <tex> $\bar{H}$</tex>-function, Mellin-Barnes type of contour integral

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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