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Elementary hypergeometric functions, Heun functions, and moments of MKZ operators

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Abstract

We consider some hypergeometric functions and prove that they are elementary functions. Consequently, the second order moments of Meyer-König and Zeller type operators are elementary functions. The higher order moments of these operators are expressed in terms of elementary functions and polylogarithms. Other applications are concerned with the expansion of certain Heun functions in series or finite sums of elementary hypergeometric functions.

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Acknowledgements

The work of the first author was financed by Lucian Blaga University of Sibiu & Hasso Plattner Foundation research grants LBUS-IRG-2020-06.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, Str. Dr. I. Ratiu, No.5-7, 550012, Sibiu, Romania

    Ana-Maria Acu

  2. Faculty of Automation and Computer Science, Department of Mathematics, Technical University of Cluj-Napoca, Str. Memorandumului nr. 28, Cluj-Napoca, Romania

    Ioan Rasa

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  1. Ana-Maria Acu
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  2. Ioan Rasa
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Correspondence to Ana-Maria Acu.

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Acu, AM., Rasa, I. Elementary hypergeometric functions, Heun functions, and moments of MKZ operators. RACSAM 115, 20 (2021). https://doi.org/10.1007/s13398-020-00943-y

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