Ellipsoidal Harmonic of the Second Kind
Ellipsoidal harmonics of the second kind, also known as Lamé functions of the second kind, are variously defined as
(Byerly 1959, p. 258) or
(Heine 1845, p. 194; Whittaker and Watson 1990, p. 562).
REFERENCES:
Byerly, W. E. "Laplace's Equation in Curvilinear Coördinates. Ellipsoidal Harmonics." Ch. 8 in An Elementary Treatise on Fourier's Series, and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics. New York: Dover, pp. 251-266, 1959.
Heine, E. "Beitrag zur Theorie der Anziehung und der Wärme." J. reine angew. Math. 29, 185-208, 1845.
Whittaker, E. T. and Watson, G. N. "Lamé Functions of the Second Kind." §23.47 in A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, pp. 562-563, 1990.
