Transformations of hypergeometric elliptic integrals

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dc.creatorVidunas, Raimundas
dc.date2008-11-28
dc.date.accessioned2026-07-07T12:06:17Z
dc.date.available2026-07-07T12:06:17Z
dc.descriptionThe paper classifies algebraic transformations of Gauss hypergeometric functions with the local exponent differences $(1/2,1/4,1/4)$, $(1/2,1/3,1/6)$ and $(1/3,1/3,1/3)$. These form a special class of algebraic transformations of Gauss hypergeometric functions, of arbitrary high degree. The Gauss hypergeometric functions can be identified as elliptic integrals on the genus 1 curves $y=x^3-x$ or $y=x^3-1$. Especially interesting are algebraic transformations of the hypergeometric functions into themselves; these transformations come from isogenies of the respective elliptic curves.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/0811.4641
dc.identifierhttp://arxiv.org/abs/0811.4641
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/208609
dc.subjectClassical Analysis and ODEs
dc.subject33C05; 34A30
dc.titleTransformations of hypergeometric elliptic integrals
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