Whittaker and Watson (1990, p. 403) define the internal and external spheroidal wavefunctions as
See also Ellipsoidal Harmonic, Oblate Spheroidal Wave Function, Prolate Spheroidal Wave Function, Spherical Harmonic
References
Abramowitz, M. and Stegun, C. A. (Eds.). ``Spheroidal Wave Functions.'' Ch. 21 in
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, pp. 751-759, 1972.
Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 642-644, 1953.
Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, 4th ed. Cambridge, England:
Cambridge University Press, 1990.