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Generalized confluent hypergeometric solutions of the Heun confluent equation

Author

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  • Ishkhanyan, T.A.
  • Ishkhanyan, A.M.

Abstract

We show that the Heun confluent equation admits infinitely many solutions in terms of the confluent generalized hypergeometric functions. For each of these solutions a characteristic exponent of a regular singularity of the Heun confluent equation is a non-zero integer and the accessory parameter obeys a polynomial equation. Each of the solutions can be written as a linear combination with constant coefficients of a finite number of either the Kummer confluent hypergeometric functions or the Bessel functions.

Suggested Citation

  • Ishkhanyan, T.A. & Ishkhanyan, A.M., 2018. "Generalized confluent hypergeometric solutions of the Heun confluent equation," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 624-630.
    • Handle: RePEc:eee:apmaco:v:338:y:2018:i:c:p:624-630
    DOI: 10.1016/j.amc.2018.06.053
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