Generalized confluent hypergeometric solutions of the Heun confluent equation

T. A. Ishkhanyan, A. M. Ishkhanyan

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)624-630
Number of pages7
JournalApplied Mathematics and Computation
Volume338
DOIs
Publication statusPublished - 1 Dec 2018

Fingerprint

Confluent Hypergeometric Function
Generalized Hypergeometric Function
Characteristic Exponents
Infinitely Many Solutions
Polynomial equation
Bessel Functions
Linear Combination
Bessel functions
Accessories
Singularity
Integer
Coefficient
Polynomials

Keywords

  • 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

Cite this

Generalized confluent hypergeometric solutions of the Heun confluent equation. / Ishkhanyan, T. A.; Ishkhanyan, A. M.

In: Applied Mathematics and Computation, Vol. 338, 01.12.2018, p. 624-630.

Research output: Contribution to journalArticle

Ishkhanyan, T. A. ; Ishkhanyan, A. M. / Generalized confluent hypergeometric solutions of the Heun confluent equation. In: Applied Mathematics and Computation. 2018 ; Vol. 338. pp. 624-630.
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