On reducing the Heun equation to the hypergeometric equation

dc.creatorMaier, Robert S.
dc.date2002-03-26
dc.date2004-08-23
dc.date.accessioned2026-07-07T04:47:17Z
dc.date.available2026-07-07T04:47:17Z
dc.descriptionThe 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.description36 pages, a few additional misprints corrected
dc.identifierhttps://arxiv.org/abs/math/0203264
dc.identifierhttp://arxiv.org/abs/math/0203264
dc.identifierJ. Differential Equations 213 (2005) 171-203
dc.identifierdoi:10.1016/j.jde.2004.07.020
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63656
dc.subjectClassical Analysis and ODEs
dc.subjectMathematical Physics
dc.subject33E30 (Primary) 34M35, 33C05 (Secondary)
dc.titleOn reducing the Heun equation to the hypergeometric equation
dc.typetext

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