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Mathieu-type series built by (p, q)-extended Gaussian hypergeometric function

최준상|Rakesh Kumar Parmar|Tibor K. Pogany
대한수학회 (The Korean Mathematical Society)|2017.05|대한수학회보 (Bulletin of the KMS)|제54권 제3호|pp. 789-797

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참고문헌

키워드

integral representations$(pq)$-extended Beta functionq)$-extended Gaussian hypergeometric functionMathieu--type seriesCahen formulabounding inequality
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초록

The main purpose of this paper is to present closed integral form expressions for the Mathieu-type $\boldsymbol a$-series and its associated alternating version whose terms contain a $(p, q)$--extended Gauss' hypergeometric function. Certain upper bounds for the two series are also given.

Abstract

The main purpose of this paper is to present closed integral form expressions for the Mathieu-type $\boldsymbol a$-series and its associated alternating version whose terms contain a $(p, q)$--extended Gauss' hypergeometric function. Certain upper bounds for the two series are also given.

참고문헌 (17)

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  6. 조용환, "THE IDEAL τ(M) AND LOCALLY CYCLIC PROJECTIVE MODULES", 호남수학학술지, 36(2), pp.339~344 (2014), 호남수학회
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  8. Y. L. Luke, "Inequalities for generalized hypergeometric functions", J. Approx. Theory, 5, pp.41~65 (1974)
  9. R. K. Parmar, "Extended Srivastava’s triple hypergeometric HA,p,q function and related bounding inequalities" (2016)
  10. T. K. Pog´any, "Integral representation of a series which includes the Mathieu a-series", J. Math. Anal. Appl, 296(1), pp.309~313 (2004)
  11. T. K. Pog´any, "Integral representation of Mathieu (a, λ)-series", Integral Transforms Spec. Funct, 16(8), pp.685~689 (2005)
  12. T. K. Pog´any, "Integral expressions for Mathieu-type series whose terms contain Fox’s H-function", Appl. Math. Lett, 20(7), pp.764~769 (2007)
  13. T. K. Pog´any, "Some Mathieu-type series for generalized H-function associated with a certain class of Feynman integrals", Integral Transforms Spec. Funct, 21(9-10), pp.765~770 (2010)
  14. T. K. Pog´any, "Some Mathieu-type series associated with the Fox-Wright function", Comput. Math. Appl, 57(1), pp.127~140 (2009)
  15. T. K. Pog´any, "Some families of Mathieu a-series and alternating Mathieu a-series", Appl. Math. Comput, 173(1), pp.69~108 (2006)
  16. T. K. Pog´any, "On Mathieu-type series whose terms contain a gener-alized hypergeometric function pFq and Meijer’s G-function", Math. Comput. Modelling, 47(9-10), pp.952~969 (2008)
  17. H. M. Srivastava, "Zeta and q-Zeta Functions and Associated Series and Integrals" (2012), Elsevier Science Publishers

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