Power series expansions for spheroidal wave functions with small arguments

摘要

Power series expansions for the angular spheroidal wave functions of the first kind Smn(c,η), with small arguments c, are derived for general integer values of m and n. The various evaluated expansion coefficients can also be used in the calculation of the corresponding angular functions of the second kind, as well as for the radial functions of any kind. Only the prolate functions are considered explicitly, but corresponding formulas for the oblate ones are obtained immediately.