Expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta and Gamma functions
| Autor: | Mariam Gevorgyan, Yevgenya Pashayan-Leroy, T. A. Ishkhanyan, Artur Ishkhanyan, Claude Leroy |
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| Přispěvatelé: | Institut de Mathématiques de Bourgogne [Dijon] (IMB), Université de Bourgogne (UB)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Bourgogne [Dijon] ( IMB ), Université de Bourgogne ( UB ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire Interdisciplinaire Carnot de Bourgogne [Dijon] (LICB), Université de Bourgogne (UB)-Université de Technologie de Belfort-Montbeliard (UTBM)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
biconfluent Heun equation
recurrence relations Recurrence relation Series (mathematics) 010308 nuclear & particles physics [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] FOS: Physical sciences General Physics and Astronomy Mathematical Physics (math-ph) 01 natural sciences 33E30 34B30 special functions Special functions Heun function 0103 physical sciences Applied mathematics [ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph] Beta (velocity) 010306 general physics Gamma function Mathematical Physics Second derivative Mathematics |
| Zdroj: | J.Contemp.Phys. J.Contemp.Phys., 2016, 51 (3), pp.229-236. ⟨10.3103/S106833721603004X⟩ J.Contemp.Phys., 2016, 51 (3), pp.229-236. 〈10.3103/S106833721603004X〉 |
| DOI: | 10.3103/S106833721603004X⟩ |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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