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Multi-parametric Le Roy function revisited

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This paper is a continuation of the recent article “Multi-parametric Le Roy function”, Fract. Calc. Appl. Anal. 26(5), 54–69 (2023), https://doi.org/10.1007/s13540-022-00119-y, by S. Rogosin and M. Dubatovskaya. Here we present further analytic properties of the Le Roy function depending on several parameters. Using the Mellin-Barnes representations we determine relations of the multi-parametric Le Roy function \(F_{(\alpha ,\beta )_m}^{(\gamma )_m}\) to the Fox H-function in the case of integer parameters \(\gamma _j\). For non-integer \(\gamma _j\) the function \(F_{(\alpha ,\beta )_m}^{(\gamma )_m}\) becomes a particular case of a new special HG-function generalizing the Fox H-function and related to other generalizations of the Fox H-function, namely \(\bar{H}\)-function and I-function (I integral). Extension to other values of the parameters \(\alpha _j,\gamma _j\) of the multi-parametric Le Roy function are discussed too. Novel formulas for double-, triple- and multiple-Laplace transform of \(F_{(\alpha ,\beta )_m}^{(\gamma )_m}\) are established. Riemann-Liouville fractional operators of the multi-parametric Le Roy function are calculated.

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Acknowledgements

This research is partially supported by the State Program of the Scientific Investigations “Convergence-2025”, grant 1.7.01.4.The authors are grateful to professor Virginia Kiryakova for the fruitful discussion of the results of the paper. Many thanks to anonymous referees for careful reading of the text and making certain important proposals.

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  1. Department of Economics, Belarusian State University, Nezavisimosti ave 4, 220030, Minsk, Belarus

    Sergei Rogosin & Maryna Dubatovskaya

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  1. Sergei Rogosin
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  2. Maryna Dubatovskaya
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Correspondence to Sergei Rogosin.

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Rogosin, S., Dubatovskaya, M. Multi-parametric Le Roy function revisited. Fract Calc Appl Anal 27, 64–81 (2024). https://doi.org/10.1007/s13540-023-00221-9

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