# Confluent Heun equations: convergence of solutions in series of coulomb wavefunctions

@article{ElJaick2013ConfluentHE, title={Confluent Heun equations: convergence of solutions in series of coulomb wavefunctions}, author={L{\'e}a Jaccoud El-Jaick and Bartolomeu D. B. Figueiredo}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2013}, volume={46} }

The Leaver solutions in series of Coulomb wavefunctions for the confluent Heun equation are given by two-sided infinite series, that is, by series where the summation index n runs from minus to plus infinity (Leaver 1986 J. Math. Phys.27 1238). First we show that, in contrast to the D’Alembert test, under certain conditions the Raabe test ensures that the domains of convergence of these solutions include an additional singular point. We also consider solutions for a limit of the confluent Heun…

## 16 Citations

Convergence and applications of some solutions of the confluent Heun equation

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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…

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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…

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- 2014

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…

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

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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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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…

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In this paper we consider the confluent Heun equation, which is a linear differential equation of second order with three singular points (two regular and one irregular). A procedure for numerical…

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We construct new solutions in series of confluent hypergeometric functions for the confluent Heun equation (CHE). Some of these solutions are applied to the one-dimensional stationary Schr\"{o}dinger…

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