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Dual Trigonometrical Series

Published online by Cambridge University Press:  18 May 2009

C. J. Tranter
C. J. Tranter
Affiliation:
Royal Military College of Science, Shrivenham.
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In a recent joint paper with J. C. Cooke [1], we have given a method of determining the coefficients an in the “dual” Fourier-Bessel series

where −1 ≤p≤, F(r) is specified and αn is a positive root of Jv(αnα) = 0. This method reduced the problem to the solution of an infinite set of algebraical equations and it was shown that, under certain circumstances, numerical values for the coefficients could be obtained fairly readily.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 4 , Issue 2 , July 1959 , pp. 49 - 57
Copyright
Copyright © Glasgow Mathematical Journal Trust 1959

References

1.Cooke, J. C. and Tranter, C. J., Dual Fourier-Bessel series, Quart. J. Mech. Appl. Math., (in press).Google Scholar
2.Tranter, C. J., On some dual integral equations, Quart. J. of Math. (Oxford) (2), 2 (1951), 60–66.Google Scholar
3.Shepherd, W. M., On trigonometrical series with mixed conditions, Proc. London Math. Soc. (2), 43 (1937), 366–375.Google Scholar
4.Magnus, W. and Oberhettinger, F. (translated by Wermer, J.), Special functions of mathematical physics (New York, 1949).Google Scholar
5.Watson, G. N., Theory of Bessel functions (Cambridge, 1944).Google Scholar
6.Whittaker, E. T. and Watson, G. N., Modern analysis (Cambridge, 1920), 229.Google Scholar
7.Erdélyi, A., Higher transcendental functions (New York, 1953), Vol. 1.Google Scholar
8.Copson, E. T., On the problem of the electrified disc, Proc. Edinburgh Math. Soc. (3), 8 (1947), 14–19.CrossRefGoogle Scholar