Some identities for spheroidal harmonics

Details Some identities for spheroidal harmonics Some identities for spheroidal harmonics

Jan 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991ap%26ss.175...51l&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 175, no. 1, Jan. 1991, p. 51-56.

Astronomy and Astrophysics

Astrophysics

2

Gravitation Theory, Legendre Functions, Spherical Harmonics, Linear Equations, Partial Differential Equations

Scientific paper

A method is presented for the derivation of the coefficient of xi-squared + eta-squared, which is shared by two spheroidal harmonics expressions, in the form of a linear combination of terms. Such identities, for which explicit formulae are exhibited in the cases of r = 1, 2, 3 and any positive or zero integers k and s, are useful in gravitational potential theory's ellipsoidal distributions when matching Legendre-function expansions are employed.

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