Generalized confluent hypergeometric solutions of the Heun confluent equation

T.A. Ishkhanyan and A.M. Ishkhanyan

Applied Mathematics and Computation, 2018, vol. 338, issue C, 624-630

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.

Keywords: Confluent Heun equation; Confluent hypergeometric function; Bessel function; Recurrence relation (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:338:y:2018:i:c:p:624-630

DOI: 10.1016/j.amc.2018.06.053

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