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Finite and Infinite Hypergeometric Sums Involving the Digamma Function

Author

Listed:
  • Juan Luis González-Santander

    (Department of Mathematics, University of Oviedo, C/ Leopoldo Calvo Sotelo 18, 33007 Oviedo, Spain
    These authors contributed equally to this work.)

  • Fernando Sánchez Lasheras

    (Department of Mathematics, University of Oviedo, C/ Leopoldo Calvo Sotelo 18, 33007 Oviedo, Spain
    These authors contributed equally to this work.)

Abstract

We calculate some finite and infinite sums containing the digamma function in closed form. For this purpose, we differentiate selected reduction formulas of the hypergeometric function with respect to the parameters applying some derivative formulas of the Pochhammer symbol. Additionally, we compare two different differentiation formulas of the generalized hypergeometric function with respect to the parameters. For some particular cases, we recover some results found in the literature. Finally, all the results have been numerically checked.

Suggested Citation

  • Juan Luis González-Santander & Fernando Sánchez Lasheras, 2022. "Finite and Infinite Hypergeometric Sums Involving the Digamma Function," Mathematics, MDPI, vol. 10(16), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2990-:d:892060
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    References listed on IDEAS

    as
    1. Alexander Apelblat, 2020. "Differentiation of the Mittag-Leffler Functions with Respect to Parameters in the Laplace Transform Approach," Mathematics, MDPI, vol. 8(5), pages 1-22, April.
    2. Alexander Apelblat & Juan Luis González-Santander, 2021. "The Integral Mittag-Leffler, Whittaker and Wright Functions," Mathematics, MDPI, vol. 9(24), pages 1-34, December.
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    Cited by:

    1. Juan Luis González-Santander & Fernando Sánchez Lasheras, 2023. "Sums Involving the Digamma Function Connected to the Incomplete Beta Function and the Bessel functions," Mathematics, MDPI, vol. 11(8), pages 1-16, April.

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