Generalized confluent hypergeometric solutions of the Heun confluent equation

T. A. Ishkhanyan, A. M. Ishkhanyan

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)624-630
Number of pages7
JournalApplied Mathematics and Computation
Publication statusPublished - 1 Dec 2018


  • 02.30.Gp Special functions
  • 02.30.Hq Ordinary differential equations
  • 02.30.Mv Approximations and expansions
  • Bessel function
  • Confluent Heun equation
  • Confluent hypergeometric function
  • Recurrence relation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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