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

@article{Melikdzhanian2021ANO, title={A note on the generalized-hypergeometric solutions of general and single-confluent Heun equations}, author={D.Yu. Melikdzhanian and Artur M. Ishkhanyan}, journal={Journal of Mathematical Analysis and Applications}, year={2021} }

## 2 Citations

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## References

SHOWING 1-10 OF 41 REFERENCES

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

- MathematicsAppl. Math. Comput.
- 2018

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

- Mathematics
- 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…

### 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…

### On Certain Solutions for Confluent and Double-Confluent Heun Equations

- Mathematics
- 2008

This paper examines some solutions for confluent and double-confluent Heun equations. In the first place, we review two Leaver's solutions in series of regular and irregular confluent hypergeometric…

### 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…

### 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…

### Convergence and applications of some solutions of the confluent Heun equation

- MathematicsAppl. Math. Comput.
- 2016

### 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…

### Integral relations for solutions of the confluent Heun equation

- MathematicsAppl. Math. Comput.
- 2015

### Solutions of the bi-confluent Heun equation in terms of the Hermite functions

- Mathematics, Physics
- 2016