Integral relations for solutions of the confluent Heun equation

@article{ElJaick2015IntegralRF,
  title={Integral relations for solutions of the confluent Heun equation},
  author={L{\'e}a Jaccoud El-Jaick and Bartolomeu D. B. Figueiredo},
  journal={Appl. Math. Comput.},
  year={2015},
  volume={256},
  pages={885-904}
}
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6 Citations
Background Citations
3
Methods Citations
1

6 Citations

Convergence and applications of some solutions of the confluent Heun equation
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We show that there exist infinitely many nontrivial choices of parameters of the single confluent Heun equation for which the three-term recurrence relations governing the expansions of the solutions…
Generalized-hypergeometric solutions of the biconfluent Heun equation
Infinitely many cases for which two independent fundamental solutions of the biconfluent Heun equation can each be presented as an irreducible linear combination of two confluent generalized…
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We use Kovacic's algorithm to obtain all Liouvillian solutions, i.e., essentially all solutions in terms of quadratures, of the master equation which governs the evolution of first order…
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References

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Integral relations and new solutions to the double-confluent Heun equation
Integral relations and transformation rules are used to obtain, out of an asymptotic solution, a new group of four pairs of solutions to the double-confluent Heun equation. Each pair presents the…
Transformations of Heun's equation and its integral relations
We find transformations of variables which preserve the form of the equation for the kernels of integral relations among solutions of the Heun equation. These transformations lead to new kernels for…
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…
Integral relations for solutions of the confluent Heun equation
Firstly, we construct kernels for integral relations among solutions of the confluent Heun equation (CHE). Additional kernels are systematically generated by applying substitutions of variables. Se...
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…
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 solutions to the confluent Heun equation and quasiexact solvability
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…
Integral relations for heun-class special functions
New integral relations are obtained for eigenfunctions produced by Heun-class equations. These relations demonstrate the duality property of the eigenfunctions with different behaviors at…
The 192 solutions of the Heun equation
TLDR
Of the 192 local solutions of the Heun equation, 24 are equivalent expressions for the local Heun function Hl, and it is shown that the resulting order-24 group of transformations of Hl is isomorphic to the symmetric group S 4 .
Ince’s limits for confluent and double-confluent Heun equations
We find pairs of solutions to a differential equation which is obtained as a special limit of a generalized spheroidal wave equation (this is also known as confluent Heun equation). One solution in…
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