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Asymptotic Expansions of Ellipsoidal Wave Functions in Terms of Hermite Functions

✍ Scribed by Harald J. W. Müller

Publisher
John Wiley and Sons
Year
1966
Tongue
English
Weight
384 KB
Volume
32
Category
Article
ISSN
0025-584X

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✦ Synopsis

Two simple pairs of asymptotic expansions in terms of Hermite functions are obtained for the'solutions of the ellipsoidal wave equation.

📜 SIMILAR VOLUMES

On Asymptotic Expansions of Ellipsoidal
On Asymptotic Expansions of Ellipsoidal Wave Functions
✍ Harald J. W. Müller 📂 Article 📅 1966 🏛 John Wiley and Sons 🌐 English ⚖ 482 KB

dn u + k cn u A . (dn u + k cn u)~'", A . ( d n u -k c n u d n u -k c n u the expansions for A (u) and A (u) being suitable for ~-dnu+(:nu i I > -; d n u h c c n u 3c B.(-. dn u ~-+ k cn -) u d n u -k c n u the expansions for H [ x (u)] and B [ z (u)] being suitable for -~ B . -\_ \_ ~ , -( dn uk cn

Small-Time Asymptotics of Hermite Functi
Small-Time Asymptotics of Hermite Functions on Compact Symmetric Spaces
✍ Jeffrey J Mitchell 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 137 KB

Let M be a compact, connected, oriented Riemannian manifold. Hermite functions on M are defined in terms of the heat kernel, and the existence of an asymptotic expansion of these functions in powers of √ t is established for small time. In the case where M is a compact symmetric space, the asymptoti