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A further note on 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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This note discusses the determination of the coefficients an in the dual trigonometrical series

where p = ± 1 and F(x), G(x) are prescribed functions of X. It is shown that this problem and the corresponding one in which the sines in equations (1) are replaced by cosines are easily reduced to a form in which the results I have recently given in this journal [1] may be applied.

As with my previous paper on this subject, the analysis is purely formal and no attempt is made to give precise conditions for which the solution is valid.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 4 , Issue 4 , September 1960 , pp. 198 - 200
Copyright
Copyright © Glasgow Mathematical Journal Trust 1960

References

1.Tranter, C. J., Dual trigonometrical series, Proc. Glasgow Math. Assoc. 4 (1959), 49–57.CrossRefGoogle Scholar
2.Watson, G. N., Theory of Bessel functions (Cambridge, 1944).Google Scholar