%0 Journal Article
%A
%A
%T Derivation of Green-type, transitional and uniform asymptotic expansions from differential equations. V. Angular oblate spheroidal wavefunctions *p̅s̅*^{r}_{n}(*η*,*h*) and *q̅s̅*^{r}_{n}(*η*,*h*) for large *h*
%D 1971
%R 10.1098/rspa.1971.0048
%J Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
%P 545-555
%V 321
%N 1547
%X The formal techniques of earlier papers (Jorna 1964a, b, 1965a, b) are applied to the differential equation for oblate spheroidal wavefunctions, y(z, h) say, with h2 large. The integro- differential equation arising in the reformulated Liouville–Green method is solved by: (i) direct iteration, yielding asymptotic expansions valid in the region │z│≃ ½π; (ii) taking its Mellin transform and solving the resulting difference equation iteratively. This approach leads to new asymptotic expansions valid for z ≃ 0 and π, and also to the more general uniform expansion. Both methods yield, concurrently, expansions for the eigenvalues and the corresponding functions themselves. As a particular application, expansions are derived for the periodic angular oblate spheroidal wavefunctions p̅s̅(z,h).
%U http://rspa.royalsocietypublishing.org/content/royprsa/321/1547/545.full.pdf