Expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta and Gamma functions
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Publication:6255968
DOI10.3103/S106833721603004XarXiv1410.8575MaRDI QIDQ6255968
M. R. Gevorgyan, A. M. Ishkhanyan, Y. Pashayan-Leroy, T. A. Ishkhanyan, C. Leroy
Publication date: 30 October 2014
Abstract: Starting from equations obeyed by 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
Other functions coming from differential, difference and integral equations (33E30) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)
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