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}
}
  • A. Ishkhanyan
  • Published 1 December 2014
  • Mathematics
  • Journal of Applied Analysis & Computation
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… 
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References

SHOWING 1-10 OF 52 REFERENCES

A SERIES SOLUTION OF THE GENERAL HEUN EQUATION IN TERMS OF INCOMPLETE BETA FUNCTIONS

We show that in the particular case when a characteristic exponent of the singularity at infinity is zero the solution of the general Heun equation can be expanded in terms of the incomplete Beta

Appell Hypergeometric Expansions of the Solutions of the General Heun Equation

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

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

Incomplete beta-function expansions of the solutions to the confluent Heun equation

Several expansions of the solutions to the confluent Heun equation in terms of incomplete beta functions are constructed. A new type of expansion involving certain combinations of the incomplete beta

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

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

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

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

NEW RELATIONS FOR THE DERIVATIVE OF THE CONFLUENT HEUN FUNCTION

The cases when the equation for the derivative of the confluent Heun function has only three singularities (in general, the equation has four such points) are examined. It is shown that this occurs

On Certain Solutions for Confluent and Double-Confluent Heun Equations

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

Solutions for the general, confluent and biconfluent Heun equations and their connection with Abel equations

In a recent paper, the canonical forms of a new multi-parameter class of Abel differential equations, the so-called Abel inverse Riccati (AIR), all of whose members can be mapped into Riccati

A limit of the confluent Heun equation and the Schrödinger equation for an inverted potential and for an electric dipole

We re-examine and extend a group of solutions in series of Bessel functions for a limiting case of the confluent Heun equation and, then, apply such solutions to the one-dimensional Schrodinger
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