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XVI.—Dual Series Relations. III. Dual Relations Involving Trigonometric Series

Published online by Cambridge University Press:  14 February 2012

R. P. Srivastav
R. P. Srivastav
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kanpur
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Synopsis

The methods developed in I, II of this series of papers are applied to a solution of a variety of dual series relations involving trigonometric series. In general the problem is reduced to one of solving (usually by numerical methods) a Fredholm integral equation of the second kind for an auxiliary function g(t), but for certain values of the parameters it is possible to obtain analytical solutions of the integral equations and these cases are considered in detail.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 66 , Issue 3 , 1963 , pp. 173 - 184
Copyright
Copyright © Royal Society of Edinburgh 1963

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References

References to Literature

Erdelyi, A. (Ed.), 1954. Tables of Integral Transforms. New York, London: McGraw-Hill.Google Scholar
Sneddon, I. N., and Srivastav, R. P., 1964. “Dual Series Relations—I. Dual Relations involving Fourier-Bessel Series.” Proc. Roy. Soc. Edin. A, 66, 150–160.Google Scholar
Srivastav, R. P., 1964. “Dual Series Relations—II. Dual Relations involving Dini Series.” Proc. Roy. Soc. Edin. A, 66, 161–172.Google Scholar
Tranter, C. J., 1959. “Dual Trigonometric Series.” Proc. Glasg. Math. Ass. 4, 49.CrossRefGoogle Scholar
Tranter, C. J., 1960. “A Further Note on Dual Trigonometrical Series.” Proc. Glasg. Math. Ass., 4, 198.CrossRefGoogle Scholar