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Generalized Hypergeometric Solutions of the Heun Equation

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Abstract

We present infinitely many solutions of the general Heun equation in terms of generalized hypergeometric functions. Each solution assumes that two restrictions are imposed on the involved parameters: acharacteristic exponent of one of the singularities must be a nonzero integer, and the accessory parameter must satisfy a polynomial equation.

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Authors and Affiliations

  1. Russian - Armenian University, Yerevan, Armenia

    A. M. Ishkhanyan

  2. Institute for Physical Research, National Academy of Sciences of Armenia, Ashtarak, Armenia

    A. M. Ishkhanyan

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  1. A. M. Ishkhanyan
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Correspondence to A. M. Ishkhanyan.

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Conflicts of interest. The author declares no conflicts of interest.

Additional information

This research was supported by the Armenian State Committee of Science (SCS Grant Nos. 18RF-139 and 18T-1C276) and the Russian — Armenian (Slavonic) University at the expense of the Ministry of Education and Science of the Russian Federation.

Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 202, No. 1, pp. 3–13, January, 2020.

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Ishkhanyan, A.M. Generalized Hypergeometric Solutions of the Heun Equation. Theor Math Phys 202, 1–10 (2020). https://doi.org/10.1134/S0040577920010018

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  • DOI: https://doi.org/10.1134/S0040577920010018

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