부산대학교 도서관

The expansions and results in the paper reviewed above [MR0143965] are generalized to the oblate spheroidal wave functions which are, after a slight transformation, solutions of the differential equation $$ y''(x)+(2m+1)\cot x\cdot y'(x)+[\Lambda_0-m(m+1)-4h^2\sin^2x]y(x)=0. $$ Three pairs of asymptotic expansions are given in terms of trigonometrical functions and of generalized Laguerre functions. Linking and normalization factors are evaluated and the asymptotic eigenvalue expansions are calculated to two more terms than known previously. The various expansions enable one to express the eigenfunctions asymptotically over the whole range $0\leq x\leq\pi$.