TL;DR
This paper proposes a numerical method for evaluating confluent Heun functions, combining power series, asymptotic expansions, and analytic continuation, with numerical tests demonstrating its effectiveness.
Contribution
It introduces a new procedure for numerically evaluating confluent Heun functions using a combined scheme of series, asymptotics, and continuation.
Findings
Numerical tests confirm the accuracy of the proposed method.
The scheme effectively handles the irregular singularity.
The approach improves computational stability for confluent Heun functions.
Abstract
In this paper we consider the confluent Heun equation, which is a linear differential equation of second order with three singular points --- two of them are regular and the third one is irregular of rank 1. The purpose of the work is to propose a procedure for numerical evaluation of the equation's solutions (confluent Heun functions). A scheme based on power series, asymptotic expansions and analytic continuation is described. Results of numerical tests are given.
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