대한수학회지 (Journal of the Korean Mathematical Society)

  • 제53권2호
  • /
  • Pages.363-379
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  • 2016
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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THE INCOMPLETE GENERALIZED τ-HYPERGEOMETRIC AND SECOND τ-APPELL FUNCTIONS

  • 투고 : 2015.02.15
  • 발행 : 2016.03.01
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초록

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [Integral Transforms Spec. Funct. 23 (2012), 659-683] and the second Appell function [Appl. Math. Comput. 219 (2013), 8332-8337] by means of the incomplete Pochhammer symbols $({\lambda};{\kappa})_{\nu}$ and $[{\lambda};{\kappa}]_{\nu}$, we introduce here the family of the incomplete generalized ${\tau}$-hypergeometric functions $2{\gamma}_1^{\tau}(z)$ and $2{\Gamma}_1^{\tau}(z)$. The main object of this paper is to study these extensions and investigate their several properties including, for example, their integral representations, derivative formulas, Euler-Beta transform and associated with certain fractional calculus operators. Further, we introduce and investigate the family of incomplete second ${\tau}$-Appell hypergeometric functions ${\Gamma}_2^{{\tau}_1,{\tau}_2}$ and ${\gamma}_2^{{\tau}_1,{\tau}_2}$ of two variables. Relevant connections of certain special cases of the main results presented here with some known identities are also pointed out.

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피인용 문헌

  1. Incomplete Caputo fractional derivative operators vol.2018, pp.1, 2018, https://doi.org/10.1186/s13662-018-1656-1
  2. Some Families of the Incomplete H-Functions and the Incomplete $$\overline H $$H¯-Functions and Associated Integral Transforms and Operators of Fractional Calculus with Applications vol.25, pp.1, 2018, https://doi.org/10.1134/S1061920818010119