Classical ellipsoidal and sphero-conal harmonics are polynomial solutions of
the Laplace equation that can be expressed in terms of Lame polynomials.
Generalized ellipsoidal and sphero-conal harmonics are polynomial solutions of
the more general Dunkl equation that can be expressed in terms of Stieltjes
polynomials. Niven's formula connecting ellipsoidal and sphero-conal harmonics
is generalized. Moreover, generalized ellipsoidal harmonics are applied to
solve the Dirichlet problem for Dunkl's equation on ellipsoids.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on
Integrable Systems and Related Topics, published in SIGMA (Symmetry,
Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
