## Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

## If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

# Derivation of Green-Type, Transitional and Uniform Asymptotic Expansions from Differential Equations. V. Angular Oblate Spheroidal Wavefunctions $\overline{ps}$nr (n, h) and $\overline{qs}$nr (n, h) for Large h

S. Jorna and C. Springer
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 321, No. 1547 (Mar. 9, 1971), pp. 545-555
Stable URL: http://www.jstor.org/stable/77813
Page Count: 11
Preview not available

## Abstract

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| ≃ 1/2π ; (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 $\overline{qs}$(z, h).

• 545
• 546
• 547
• 548
• 549
• 550
• 551
• 552
• 553
• 554
• 555