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Degenerate Analogues of Euler Zeta, Digamma, and Polygamma Functions

Author

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  • Fuli He
  • Ahmed Bakhet
  • Mohamed Akel
  • Mohamed Abdalla

Abstract

In recent years, much attention has been paid to the role of degenerate versions of special functions and polynomials in mathematical physics and engineering. In the present paper, we introduce a degenerate Euler zeta function, a degenerate digamma function, and a degenerate polygamma function. We present several properties, recurrence relations, infinite series, and integral representations for these functions. Furthermore, we establish identities involving hypergeometric functions in terms of degenerate digamma function.

Suggested Citation

  • Fuli He & Ahmed Bakhet & Mohamed Akel & Mohamed Abdalla, 2020. "Degenerate Analogues of Euler Zeta, Digamma, and Polygamma Functions," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-9, May.
    • Handle: RePEc:hin:jnlmpe:8614841
    DOI: 10.1155/2020/8614841
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    Cited by:

    1. Mohammed Z. Alqarni & Mohamed Abdalla, 2023. "Novel Kinds of Fractional λ –Kinetic Equations Involving the Generalized Degenerate Hypergeometric Functions and Their Solutions Using the Pathway-Type Integral," Mathematics, MDPI, vol. 11(19), pages 1-14, October.

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