# Heun Functions and Some of Their Applications in Physics

@article{Hortasu2011HeunFA, title={Heun Functions and Some of Their Applications in Physics}, author={M. Hortaçsu}, journal={Advances in High Energy Physics}, year={2011} }

Most of the theoretical physics known today is described by using a small number of differential equations. For linear systems, different forms of the hypergeometric or the confluent hypergeometric equations often suffice to describe the system studied. These equations have power series solutions with simple relations between consecutive coefficients and/or can be represented in terms of simple integral transforms. If the problem is nonlinear, one often uses one form of the Painlevé equations…

## 76 Citations

### 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…

### An application of the HeunB function

- Physics
- 2022

: How does the inclusion of the gravitational potential alter an otherwise exact quantum mechanical result? This question motivates this report, with the answer determined from an edited version of…

### Special functions emerging from symmetries of the space of solutions to special double confluent Heun equation

- MathematicsEuropean Journal of Mathematics
- 2022

A family of quadruplets of interrelated functions holomorphic on the universal cover of the complex plane without zero (for brevity, -functions) distinguished by certain noteworthy properties is…

### Solution Space Monodromy of a Special Double Confluent Heun Equation and Its Applications

- MathematicsTheoretical and Mathematical Physics
- 2019

We consider three linear operators determining automorphisms of the solution space of a special double confluent Heun equation of positive integer order (L-operators). We propose a new method for…

### Closed-form solution of a general three-term recurrence relation: applications to Heun functions and social choice models

- Mathematics
- 2023

We derive a concise closed-form solution for a linear three-term recurrence relation. Such recurrence relations are very common in the quantitative sciences, and describe finite difference schemes,…

### On the solutions of linear Volterra equations of the second kind with sum kernels

- MathematicsArXiv
- 2019

This work considers a linear Volterra integral equation of the second kind with a sum kernel and gives the solution of the equation in terms of solutions of the separate equations with kernels, obtaining a novel series representation for the solution with improved convergence properties.

### Orthogonal polynomials, asymptotics, and Heun equations

- MathematicsJournal of Mathematical Physics
- 2019

The Painleve equations arise from the study of Hankel determinants generated by moment matrices, whose weights are expressed as the product of ``classical" weights multiplied by suitable…

### Elementary integral series for Heun functions: Application to black-hole perturbation theory

- MathematicsJournal of Mathematical Physics
- 2022

Heun differential equations are the most general second order Fuchsian equations with four regular singularities. An explicit integral series representation of Heun functions involving only…

### A Lanczos-like method for non-autonomous linear ordinary differential equations

- Computer Science, MathematicsBollettino dell'Unione Matematica Italiana
- 2022

This paper explains how the Lanczos algorithm is built from a generalization of Krylov subspaces, and it proves crucial properties, such as the matching moment property, which is at the heart of much system dynamics, control theory, and model reduction problems.

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