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A New Representation of the k-Gamma Functions

Author

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  • Asifa Tassaddiq

    (College of Computer and Information Sciences, Majmaah University, Majmaah 11952, Saudi Arabia)

Abstract

The products of the form z ( z + l ) ( z + 2 l ) … ( z + ( k − 1 ) l ) are of interest for a wide-ranging audience. In particular, they frequently arise in diverse situations, such as computation of Feynman integrals, combinatory of creation, annihilation operators and in fractional calculus. These expressions can be successfully applied for stated applications by using a mathematical notion of k-gamma functions. In this paper, we develop a new series representation of k-gamma functions in terms of delta functions. It led to a novel extension of the applicability of k-gamma functions that introduced them as distributions defined for a specific set of functions.

Suggested Citation

  • Asifa Tassaddiq, 2019. "A New Representation of the k-Gamma Functions," Mathematics, MDPI, vol. 7(2), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:133-:d:202499
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    References listed on IDEAS

    as
    1. M. Aslam Chaudhry & Asghar Qadir, 2004. "Fourier transform and distributional representation of the gamma function leading to some new identities," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-6, January.
    2. Set, Erhan & Tomar, Muharrem & Sarikaya, Mehmet Zeki, 2015. "On generalized Grüss type inequalities for k-fractional integrals," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 29-34.
    3. Marie-Louise Lackner & Martin Lackner, 2017. "On the likelihood of single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 717-745, April.
    4. Al-Lail, Mohammed H. & Qadir, Asghar, 2015. "Fourier transform representation of the generalized hypergeometric functions with applications to the confluent and Gauss hypergeometric functions," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 392-397.
    Full references (including those not matched with items on IDEAS)

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