# Expansions of the solutions to the confluent Heun equation in terms of the Kummer confluent hypergeometric functions

@article{Ishkhanyan2014ExpansionsOT, title={Expansions of the solutions to the confluent Heun equation in terms of the Kummer confluent hypergeometric functions}, author={T. A. Ishkhanyan and Artur M. Ishkhanyan}, journal={arXiv: Classical Analysis and ODEs}, year={2014} }

We examine the series expansions of the solutions of the confluent Heun equation in terms of three different sets of the Kummer confluent hypergeometric functions. The coefficients of the expansions in general obey three-term recurrence relations defining double-sided infinite series; however, four-term and two-term relations are also possible in particular cases. The conditions for left- and/or right-side termination of the derived series are discussed.

## 27 Citations

### Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions

- Mathematics
- 2015

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 variables of the…

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- MathematicsJournal of Physics: Conference Series
- 2019

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 expansions of the solutions…

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### Confluent hypergeometric expansions of the solutions of the double-confluent Heun equation

- Mathematics
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Several expansions of the solutions of the double-confluent Heun equation in terms of the Kummer confluent hypergeometric functions are presented. Three different sets of these functions are…

### Expansions of the Solutions of the General Heun Equation Governed by Two-Term Recurrence Relations for Coefficients

- MathematicsAdvances in High Energy Physics
- 2018

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 which differ from…

### A note on the generalized-hypergeometric solutions of general and single-confluent Heun equations

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- 2021

### Generalized confluent hypergeometric solutions of the Heun confluent equation

- MathematicsAppl. Math. Comput.
- 2018

### Appell Hypergeometric Expansions of the Solutions of the General Heun Equation

- Mathematics
- 2014

Starting from a second-order Fuchsian differential equation having five regular singular points, an equation obeyed by a function proportional to the first derivative of the solution of the Heun…

### SERIES SOLUTIONS OF CONFLUENT HEUN EQUATIONS IN TERMS OF INCOMPLETE GAMMA-FUNCTIONS

- MathematicsJournal of Applied Analysis & Computation
- 2019

We present a simple systematic algorithm for construction of expansions of the solutions of ordinary differential equations with rational coefficients in terms of mathematical functions having…

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

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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…

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