On reducing the Heun equation to the hypergeometric equation
| dc.creator | Maier, Robert S. | |
| dc.date | 2002-03-26 | |
| dc.date | 2004-08-23 | |
| dc.date.accessioned | 2026-07-07T04:47:17Z | |
| dc.date.available | 2026-07-07T04:47:17Z | |
| dc.description | The reductions of the Heun equation to the hypergeometric equation by polynomial transformations of its independent variable are enumerated and classified. Heun-to-hypergeometric reductions are similar to classical hypergeometric identities, but the conditions for the existence of a reduction involve features of the Heun equation that the hypergeometric equation does not possess; namely, its cross-ratio and accessory parameters. The reductions include quadratic and cubic transformations, which may be performed only if the singular points of the Heun equation form a harmonic or an equianharmonic quadruple, respectively; and several higher-degree transformations. This result corrects and extends a theorem in a previous paper, which found only the quadratic transformations. [See K. Kuiken, "Heun's equation and the hypergeometric equation", SIAM Journal on Mathematical Analysis 10:3 (1979), 655-657.] | |
| dc.description | 36 pages, a few additional misprints corrected | |
| dc.identifier | https://arxiv.org/abs/math/0203264 | |
| dc.identifier | http://arxiv.org/abs/math/0203264 | |
| dc.identifier | J. Differential Equations 213 (2005) 171-203 | |
| dc.identifier | doi:10.1016/j.jde.2004.07.020 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63656 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 33E30 (Primary) 34M35, 33C05 (Secondary) | |
| dc.title | On reducing the Heun equation to the hypergeometric equation | |
| dc.type | text |