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Prabhakar Functions of Le Roy Type: Inequalities and Asymptotic Formulae

Author

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  • Jordanka Paneva-Konovska

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria)

Abstract

In this paper, the four-index generalization of the classical Le Roy function is considered on a wider set of parameters and its order and type are given. Letting one of the parameters take non-negative integer values, a family of functions with such a type of index is constructed. The behaviour of these functions is studied in the complex plane C and in different domains thereof. First, several inequalities are obtained in C , and then they are modified on its compact subsets as well. Moreover, an asymptotic formula is proved for ‘large’ values of the indices of these functions. Additionally, the multi-index analogue of the abovementioned four-index Le Roy type function is considered and its basic properties are obtained. Finally, several special cases of the two functions under consideration are discussed.

Suggested Citation

  • Jordanka Paneva-Konovska, 2023. "Prabhakar Functions of Le Roy Type: Inequalities and Asymptotic Formulae," Mathematics, MDPI, vol. 11(17), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3768-:d:1231358
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    References listed on IDEAS

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    1. Jordanka Paneva-Konovska, 2021. "Series in Le Roy Type Functions: A Set of Results in the Complex Plane—A Survey," Mathematics, MDPI, vol. 9(12), pages 1-15, June.
    2. Virginia Kiryakova, 2021. "A Guide to Special Functions in Fractional Calculus," Mathematics, MDPI, vol. 9(1), pages 1-40, January.
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    Cited by:

    1. Jordanka Paneva-Konovska & Virginia Kiryakova, 2024. "The Generalized Fox–Wright Function: The Laplace Transform, the Erdélyi–Kober Fractional Integral and Its Role in Fractional Calculus," Mathematics, MDPI, vol. 12(12), pages 1-25, June.
    2. Virginia Kiryakova & Jordanka Paneva-Konovska, 2024. "Going Next after “A Guide to Special Functions in Fractional Calculus”: A Discussion Survey," Mathematics, MDPI, vol. 12(2), pages 1-39, January.

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