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Some triple trigonometrical series

Published online by Cambridge University Press:  18 May 2009

C. J. Tranter
C. J. Tranter
Affiliation:
Royal Military Collegeof Science Shrivenham
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This paper considers the determination of the coefficients in two sets of triple trigonometrical series and shows that these can be obtained in closed form. The series considered are special cases of some triple series in Jacobi polynomials studied by K. N. Srivastava [1]. Srivastava, however, shows that the problem for the more general series can be reduced to the solution of a Fredholm integral equation of the second kind and he does not discuss special cases which may lead to closed form solutions.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 10 , Issue 2 , July 1969 , pp. 121 - 125
Copyright
Copyright © Glasgow Mathematical Journal Trust 1969

References

REFERENCES

1.Srivastava, K. N., On triple integral series equations involving series of Jacobi polynomials, Proc. Edinburgh Math. Soc. 15 (1967), 221–231.CrossRefGoogle Scholar
2.Williams, W. E., Note on the reduction of dual and triple series equations to dual and triple integral equations, Proc. Cambridge Philos. Soc. 59 (1963), 731–734.CrossRefGoogle Scholar
3.Tranter, C. J., Some triple integral equations, Proc. Glasgow Math. Assoc. 4 (1960), 200–203.CrossRefGoogle Scholar
4.Watson, G. N., Theory of Bessel functions (Cambridge, 1944).Google Scholar
5.Sneddon, I. N., Mixed boundary value problems in potential theory (New York, 1966).Google Scholar