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On Asymptotic Expansions of Ellipsoidal Wave Functions
Author(s) -
Müller Harald J. W.
Publication year - 1966
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19660320305
Subject(s) - mathematics , hermite polynomials , jacobian matrix and determinant , normalization (sociology) , elliptic function , ellipsoid , mathematical analysis , asymptotic expansion , method of matched asymptotic expansions , differential equation , physics , astronomy , sociology , anthropology
In two previous papers it was shown that three pairs of asymptotic expansions exist for the solutions of the ellipsoidal wave equation: One pair in terms of Jacobian elliptic functions and two pairs in terms of Hermite functions. In the present investigation we show that the expansions can be joined in regions of common validity. We then identify these solutions with known functions, and finally derive asymptotic expansions for their normalization constants.