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I recently started to study problems with prolate spheroidal geometries, for which prolate spheroidal coordinates are most suited. In particular I have the advantage that the problem is axisymmetric around the spheroid major axis.

While I'm used to Spherical Harmonics expansions and also to solutions of Laplace equation in terms of Spherical Harmonics I'm not used to spheroidal coordinates and spheroidal harmonics.

Specifically i'm looking for some reference on spheroidal harmonics, and how to expand scalar functions in terms of spheroidal harmonics. Do you have any reading to suggest me? Perhaps a book? I couldn't find anything useful with a (rather) quick search on google.

PS I am an engineer so I don't want to go deep into the geometry and mathematical details of spheroidal coordinates and harmonics, i only need a way to solve a biharmonic scalar equation in these coordinates

Thanks in advance.

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    $\begingroup$ This might be a good place to start. NIST dlmf.nist.gov/30.13#iv $\endgroup$ – DisintegratingByParts Jan 3 '16 at 16:17
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    $\begingroup$ Thanks, i'll give a look to that link. I'm also giving a look to the following book: "ellipsoidal harmonics: Theory and applications" $\endgroup$ – SSC Napoli Jan 3 '16 at 16:19
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    $\begingroup$ I was looking around at the NIST site, and the link I ended up giving you was not the top level one for the subject. This is a better starting point on the NIST site dlmf.nist.gov/30 . Thanks for your reference.. $\endgroup$ – DisintegratingByParts Jan 3 '16 at 16:24
  • $\begingroup$ Have you reached an answear to your question. Please , post here $\endgroup$ – Jose Enrique Calderon Apr 9 at 10:20

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