Generalized Umemura polynomials

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dc.creatorKirillov, Anatol N.
dc.creatorTaneda, Makoto
dc.date2000-10-28
dc.date.accessioned2026-07-07T04:38:18Z
dc.date.available2026-07-07T04:38:18Z
dc.descriptionWe introduce and study generalized Umemura polynomials $U_{n,m}^{(k)}(z,w;a,b)$ which are a natural generalization of the Umemura polynomials $U_n(z,w;a,b)$ related to Painlevé $VI$ equation. We will show that if $a=b$, or $a=0$, or $b=0$ then polynomials $U_{n,m}^{(0)}(z,w;a,b)$ generate solutions to Painlevé $VI$. We will describe a connection between polynomials $U_{n,m}^{(0)}(z,w;a,0)$ and certain Umemura polynomials $U_k(z,w;α,β)$.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0010279
dc.identifierhttp://arxiv.org/abs/math/0010279
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60228
dc.subjectCombinatorics
dc.subjectQuantum Algebra
dc.subject14D15;34M55
dc.titleGeneralized Umemura polynomials
dc.typetext

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