Expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta and Gamma functions
- Authors: Ishkhanyan T.A.1,2, Pashayan-Leroy Y.3, Gevorgyan M.R.1,3, Leroy C.3, Ishkhanyan A.M.1
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Affiliations:
- Institute for Physical Research
- Moscow Institute of Physics and Technology
- Laboratoire Interdisciplinaire Carnot de Bourgogne
- Issue: Vol 51, No 3 (2016)
- Pages: 229-236
- Section: Article
- URL: https://journals.rcsi.science/1068-3372/article/view/228045
- DOI: https://doi.org/10.3103/S106833721603004X
- ID: 228045
Cite item
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.
About the authors
T. A. Ishkhanyan
Institute for Physical Research; Moscow Institute of Physics and Technology
Author for correspondence.
Email: tishkhanyan@gmail.com
Armenia, Ashtarak; Dolgoprudny
Y. Pashayan-Leroy
Laboratoire Interdisciplinaire Carnot de Bourgogne
Email: tishkhanyan@gmail.com
France, Bourgogne
M. R. Gevorgyan
Institute for Physical Research; Laboratoire Interdisciplinaire Carnot de Bourgogne
Email: tishkhanyan@gmail.com
Armenia, Ashtarak; Bourgogne
C. Leroy
Laboratoire Interdisciplinaire Carnot de Bourgogne
Email: tishkhanyan@gmail.com
France, Bourgogne
A. M. Ishkhanyan
Institute for Physical Research
Email: tishkhanyan@gmail.com
Armenia, Ashtarak