Jacobi elliptic coordinates, functions of Heun and Lame type and the Niven transform

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dc.contributor.authorKalnins, Ernie G.
dc.contributor.authorMiller, W., Jr.
dc.date.accessioned2009-12-02T20:56:39Z
dc.date.available2009-12-02T20:56:39Z
dc.date.issued2005
dc.description.abstractLame and Heun functions arise via separation of the Laplace equation in general Jacobi ellipsoidal or conical coordinates. In contrast to hypergeometric functions that also arise via variable separation in the Laplace equation, Lame and Heun functions have received relatively little attention, since they are rather intractable. Nonetheless functions of Heun type do have remarkable properties, as was pointed out in the classical book \Modern Analysis" by Whittaker and Watson who devoted an entire chapter to the subject. Unfortunately the beautiful identities appearing in this chapter have received little notice, probably because the methods of proof seemed obscure. In this paper we apply the modern operator characterization of variable separation and exploit the conformal symmetry of the Laplace equation to obtain product identities for Heun type functions. We interpret the Niven transform as an intertwining operator under the action of the conformal group. We give simple operator derivations of some of the basic formulas presented by Whittaker and Watson and then show how to generalize their results to more complicated situations and to higher dimensions.en
dc.format.mimetypeapplication/pdf
dc.identifier.citationKalnins, E. G. & Miller, W. Jr. (2005). Jacobi elliptic coordinates, functions of Heun and Lame type and the Niven transform. Regular and Chaotic Dynamics, 10(4), 487-508.en
dc.identifier.doi10.1070/RD2005v010n04ABEH000327en
dc.identifier.urihttps://hdl.handle.net/10289/3453
dc.language.isoen
dc.publisherTurpion Ltden_NZ
dc.relation.isPartOfRegular and chaotic dynamicsen_NZ
dc.relation.urihttp://www.turpion.org/php/full/infoFT.phtml?journal_id=rd&paper_id=327en
dc.rightsThis article has been published in the journal: Regular and Chaotic Dynamics. Used with permission.en
dc.subjectLame and Heun functionen
dc.subjectmathsen
dc.subjectmathematicsen
dc.subjectLaplace equationen
dc.subjectJacobi ellipsoidalen
dc.titleJacobi elliptic coordinates, functions of Heun and Lame type and the Niven transformen
dc.typeJournal Articleen
pubs.begin-page487en_NZ
pubs.elements-id31236
pubs.end-page508en_NZ
pubs.issue4en_NZ
pubs.volume10en_NZ
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