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On the solution of a Riesz equilibrium problem and integral identities for special functions

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorChafai, Djalil
HAL ID: 11025
ORCID: 0000-0002-1446-1428
hal.structure.identifierCenter for Constructive Approximation [Vanderbilt]
dc.contributor.authorSaff, Edward B.
hal.structure.identifierSchool of Mathematics and Statistics [Sydney] [UNSW]
dc.contributor.authorWomersley, Robert S.
dc.date.accessioned2021-12-10T14:40:04Z
dc.date.available2021-12-10T14:40:04Z
dc.date.issued2021
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22354
dc.language.isoenen
dc.subject.ddc519en
dc.titleOn the solution of a Riesz equilibrium problem and integral identities for special functionsen
dc.typeDocument de travail / Working paper
dc.description.abstractenThe aim of this note is to provide a quadratic external field extension of a classical result of Marcel Riesz for the equilibrium measure on a ball with respect to Riesz s-kernels, including the logarithmic kernel, in arbitrary dimensions. The equilibrium measure is a radial arcsine distribution. As a corollary, we obtain new integral identities involving special functions such as elliptic integrals and more generally hypergeometric functions. These identities are not found in the existing tables for series and integrals, and are not recognized by advanced mathematical software. Among other ingredients, our proofs involve the Euler-Lagrange variational characterization, the Funk-Hecke formula, and the Weyl lemma for the regularity of elliptic equations.en
dc.identifier.citationpages21en
dc.relation.ispartofseriestitleCahier de recherche du CEREMADEen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-03312868en
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.identifier.citationdate2021
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2021-12-10T14:34:06Z
hal.author.functionaut
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