Generalized spheroidal wave equation and limiting cases
| dc.creator | Figueiredo, B. D. Bonorino | |
| dc.date | 2006-11-19 | |
| dc.date | 2006-12-12 | |
| dc.date.accessioned | 2026-07-07T07:48:44Z | |
| dc.date.available | 2026-07-07T07:48:44Z | |
| dc.description | We find sets of solutions to the generalized spheroidal wave equation (GSWE) or, equivalently, to the confluent Heun equation. Each set is constituted by three solutions, one given by a series of ascending powers of the independent variable, and the others by series of regular and irregular confluent hypergeometric functions. For a fixed set, the solutions converge over different regions of the complex plane but present series coefficients proportional to each other. These solutions for the GSWE afford solutions to a double-confluent Heun equation by a taking-limit process due to Leaver. Another procedure, called Whittaker-Ince limit, provides solutions in series of powers and Bessel functions for two other equations with a different type of singularity at infinity. In addition, new solutions are obtained for the Whittaker-Hill and Mathieu equations by considering these as special cases of both the confluent and double-confluent Heun equations. In particular, we find that each of the Lindmann-Stieltjes solutions for the Mathieu equation is associated with two expansions in series of Bessel functions. We also discuss a set of solutions in series of hypergeometric and confluent hypergeometric functions for the GSWE and use their Leaver limits to obtain infinite-series solutions for the Schrödinger equation with an asymmetric double-Morse potential. Finally, the possibility of extending the solutions of the GSWE to the general Heun equation is briefly discussed. | |
| dc.description | Submitted to Journal of Mathematical Physics | |
| dc.identifier | https://arxiv.org/abs/math-ph/0611048 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0611048 | |
| dc.identifier | J.Math.Phys. 48 (2007) 013503 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124604 | |
| dc.subject | Mathematical Physics | |
| dc.title | Generalized spheroidal wave equation and limiting cases | |
| dc.type | text |