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

@article{Ishkhanyan2019SERIESSO, title={SERIES SOLUTIONS OF CONFLUENT HEUN EQUATIONS IN TERMS OF INCOMPLETE GAMMA-FUNCTIONS}, author={Artur M. Ishkhanyan}, journal={Journal of Applied Analysis \& Computation}, year={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 indefinite integral representation. The approach employs an auxiliary equation involving only the derivatives of a solution of the equation under consideration. Using power-series expansions of the solutions of this auxiliary equation, we construct several expansions of the four confluent Heun equations…

## 3 Citations

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

- MathematicsJournal of Mathematical Analysis and Applications
- 2021

### A new class of approximate analytical solutions of the Pridmore-Brown equation

- MathematicsJournal of Mathematical Physics
- 2022

There is only a limited amount of known analytical solutions to the Pridmore-Brown equation, mostly employing asymptotic behavior for a certain frequency limit and specifically chosen flow profiles.…

### Generalized-hypergeometric solutions of the biconfluent Heun equation

- MathematicsThe Ramanujan Journal
- 2021

Infinitely many cases for which two independent fundamental solutions of the biconfluent Heun equation can each be presented as an irreducible linear combination of two confluent generalized…

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