External Ellipsoidal Harmonics for the Dunkl-Laplacian

Hans Volkmer

doi:10.3842/SIGMA.2008.091

External Ellipsoidal Harmonics for the Dunkl-Laplacian

Classical Analysis and ODEs 2008-12-24 v1 Mathematical Physics math.MP

Authors: Hans Volkmer

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Abstract

The paper introduces external ellipsoidal and external sphero-conal $h$ -harmonics for the Dunkl-Laplacian. These external $h$ -harmonics admit integral representations, and they are connected by a formula of Niven's type. External $h$ -harmonics in the plane are expressed in terms of Jacobi polynomials $P_n^{\alpha,\beta}$ and Jacobi's functions $Q_n^{\alpha,\beta}$ of the second kind.

Keywords

jacobi forms

Cite

@article{arxiv.0812.4365,
  title  = {External Ellipsoidal Harmonics for the Dunkl-Laplacian},
  author = {Hans Volkmer},
  journal= {arXiv preprint arXiv:0812.4365},
  year   = {2008}
}

Comments

This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

External Ellipsoidal Harmonics for the Dunkl-Laplacian

Abstract

Keywords

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