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Expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta and Gamma functions

  • T. A. IshkhanyanEmail author
  • Y. Pashayan-Leroy
  • M. R. Gevorgyan
  • C. Leroy
  • A. M. Ishkhanyan
Article

Abstract

Considering the equations for some functions involving the first or the second derivatives of the biconfluent Heun function, we construct two expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta functions. The first series applies single Beta functions as expansion functions, while the second one involves a combination of two Beta functions. The coefficients of expansions obey four- and five-term recurrence relations, respectively. It is shown that the proposed technique is potent to produce series solutions in terms of other special functions. Two examples of such expansions in terms of the incomplete Gamma functions are presented.

Keywords

biconfluent Heun equation special functions recurrence relations 

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Copyright information

© Allerton Press, Inc. 2016

Authors and Affiliations

  • T. A. Ishkhanyan
    • 1
    • 2
    Email author
  • Y. Pashayan-Leroy
    • 3
  • M. R. Gevorgyan
    • 1
    • 3
  • C. Leroy
    • 3
  • A. M. Ishkhanyan
    • 1
  1. 1.Institute for Physical ResearchNAS of ArmeniaAshtarakArmenia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyRussia
  3. 3.Laboratoire Interdisciplinaire Carnot de BourgogneUniversité de BourgogneBourgogneFrance

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