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An improved method for 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 previous paper in this journal [1], I gave formulae for determining the coefficients in certain dual trigonometrical series. The derivation of these formulae involved rather sophisticated assumptions and some intricate manipulation of the hypergeometric function and relied heavily on the solution of Schlömilch's integral equation. I have now found a much simpler formal solution by using Mehler's integral representation of the Legendre polynomial and the final formulae for the coefficients can be given in a more attractive form. As the results of my previous work have had several recent applications to physical problems, it seems worth while to give some details of this improved solution.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 6 , Issue 3 , January 1964 , pp. 136 - 140
Copyright
Copyright © Glasgow Mathematical Journal Trust 1964

References

REFERENCES

1.Tranter, C. J., Dual trigonometrical series, Proc. Glasgow Math. Assoc. 4 (1959), 49–57.CrossRefGoogle Scholar
2.Magnus, W. and Oberhettinger, F. (translated by Wermer, J.), Special functions of mathematical physics (New York, 1949).Google Scholar