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Inversion of the Struve transform of half integer order

Published online by Cambridge University Press:  17 February 2009

B. H. J. McKellar ,
M. A. Box  and
E. R. Love
B. H. J. McKellar
Affiliation:
School of Physics, University of Melbourne, Parkville, Victoria 3052 (permanent address) and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, U.S.A.
M. A. Box
Affiliation:
School of Physics, University of New South Wales, Kensington, N.S.W. 2033.
E. R. Love
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria 3052.
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Abstract

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Defining a spherical Struve function we show that the Struve transform of half integer order, or spherical Struve transform,

where n is a non-negative integer, may under suitable conditions be solved for f(t):

where is the sum of the first n + 1 terms in the asymptotic expansion of φn(x) as x → ∞. The coefficients in the asymptotic expansion are identified as

It is further shown that functions φn (x) which are representable as spherical Struve transforms satisfy n + 1 integral constraints, which in turn allow the construction of many equivalent inversion formulae.

Type
Research Article
Information
The ANZIAM Journal , Volume 25 , Issue 2 , October 1983 , pp. 161 - 174
Copyright
Copyright © Australian Mathematical Society 1983

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