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

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Journal of Contemporary Physics (Armenian Academy of Sciences) Aims and scope

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.

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Author information

Authors and Affiliations

  1. Institute for Physical Research, NAS of Armenia, Ashtarak, Armenia

    T. A. Ishkhanyan, M. R. Gevorgyan & A. M. Ishkhanyan

  2. Moscow Institute of Physics and Technology, Dolgoprudny, Russia

    T. A. Ishkhanyan

  3. Laboratoire Interdisciplinaire Carnot de Bourgogne, Université de Bourgogne, Bourgogne, France

    Y. Pashayan-Leroy, M. R. Gevorgyan & C. Leroy

Authors
  1. T. A. Ishkhanyan
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  2. Y. Pashayan-Leroy
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  3. M. R. Gevorgyan
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  4. C. Leroy
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  5. A. M. Ishkhanyan
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Corresponding author

Correspondence to T. A. Ishkhanyan.

Additional information

Original Russian Text © T.A. Ishkhanyan, Y. Pashayan-Leroy, M.R. Gevorgyan, C. Leroy, A.M. Ishkhanyan, 2016, published in Izvestiya Natsional’noi Akademii Nauk Armenii, Fizika, 2016, Vol. 51, No. 3, pp. 313–322.

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Ishkhanyan, T.A., Pashayan-Leroy, Y., Gevorgyan, M.R. et al. Expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta and Gamma functions. J. Contemp. Phys. 51, 229–236 (2016). https://doi.org/10.3103/S106833721603004X

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  • DOI: https://doi.org/10.3103/S106833721603004X

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