A study of (R)-1 expansions in oblate coordinates
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A short Word document dated 6.27.10 and signed PhL. It is a placeholder for a result derived in Phil's document on the Smythe method for Green's functions (cone examples, Appendix D) and verified against Smythe. It gives 1/R as a double sum over n and m of Legendre functions Pnm and Qnm with cos(m[φ-φ0]). It also notes, from Appendix E of that document, that each term is real.
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A study of 1/R expansions in oblate spheroidal coordinates PhL 6.27.10
I have not written this little doc yet, but I want to have a stub to hold the result which I derived in the document "the Smythe method for Green's Functions, cone examples.doc" Appendix D, and which is verified by Smythe:
1/R = j Σn=0∞Σm=0n (-1)m (εm/c1) (2n+1) f(n,-m)2Qnm(jζ>) Pnm(jζ<) Pnm(ξ) Pnm(ξ0) cos(m[φ-φ0])
In Appendix E of that same doc I show that Qnm(jζ>) Pnm(jζ<) is pure imaginary, so that each term in the above double sum is in fact real.