291 citations
- National Academy of Sciences of ArmeniaAM59 papers
- Centre National de la Recherche ScientifiqueFR44 papers
- Laboratoire Interdisciplinaire Carnot de BourgogneFR39 papers
- Yerevan State UniversityAM34 papers
- Université de BourgogneFR32 papers
- Moscow Institute of Physics and TechnologyRU28 papers
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8 papers · 1 filter
A note on the generalized-hypergeometric solutions of general and single-confluent Heun equations
D. Yu. Melikdzhanian, A. M. Ishkhanyan
We review the series solutions of the general and single-confluent Heun equations in terms of powers, ordinary-hypergeometric and confluent-hypergeometric functions. The conditions…
From Heun Class Equations to Painlevé Equations
Jan Dereziński, Artur Ishkhanyan, Adam Latosiński
In the first part of our paper we discuss linear 2nd order differential equations in the complex domain, especially Heun class equations, that is, the Heun equation and its conflue…
Confluent hypergeometric expansions of the confluent Heun function governed by two-term recurrence relations
T. A. Ishkhanyan, V. P. Krainov, A. M. Ishkhanyan
We show that there exist infinitely many nontrivial choices of parameters of the single confluent Heun equation for which the three-term recurrence relations governing the expansio…
Generalized hypergeometric solutions of the Heun equation
A. M. Ishkhanyan
We present infinitely many solutions of the general Heun equation in terms of generalized hypergeometric functions. Each solution assumes that two restrictions are imposed on the i…
Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions
C. Leroy, A. M. Ishkhanyan
We construct several expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta functions and the Appell generalized hypergeometric functions of two…
Expansions of the solutions of the general Heun equation governed by two-term recurrence relations for coefficients
T. A. Ishkhanyan, T. A. Shahverdyan, A. M. Ishkhanyan
We examine the expansions of the solutions of the general Heun equation in terms of the Gauss hypergeometric functions. We present several expansions using functions, the forms of…