An improved method for dual trigonometrical series

C. J. Tranter

doi:10.1017/S2040618500034900

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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.

References

REFERENCES

1.Tranter, C. J., Dual trigonometrical series, Proc. Glasgow Math. Assoc. 4 (1959), 49–57.CrossRef Google Scholar

2.Magnus, W. and Oberhettinger, F. (translated by Wermer, J.), Special functions of mathematical physics (New York, 1949).Google Scholar

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An improved method for dual trigonometrical series

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