Access

You are not currently logged in.

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

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

Derivation of Green-Type, Transitional and Uniform Asymptotic Expansions from Differential Equations. V. Angular Oblate Spheroidal Wavefunctions $\overline{ps}$ n r (n, h) and $\overline{qs}$ n r (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
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/77813
Page Count: 11
  • Read Online (Free)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
Derivation of Green-Type, Transitional and Uniform Asymptotic Expansions from Differential Equations. V. Angular Oblate Spheroidal Wavefunctions $\overline{ps}$
n
r (n, h) and $\overline{qs}$
n
r (n, h) for Large h
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).

Page Thumbnails

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