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XIX.—Some Triple Trigonometrical Series Equations and their Application

Published online by Cambridge University Press:  14 February 2012

K. S. Parihar
Affiliation:
Department of Mathematics, Indian Institute of Technology, Bombay, India

Synopsis

Closed form solutions of some triple equations involving trigonometric series have been obtained, in each case, by reducing them to a single integral equation. The results have been applied to determine the distribution of stress in the interior of an infinitely long elastic strip containing a pair of Griffith cracks situated on a line perpendicular to the bounding lines of the strip.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1971

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References

References to Literature

[1]Cooke, J. C., 1970. ‘The solution of some integral equations and their connection with dual integral equations and series’, Glasg. Math. J., 11, 920.CrossRefGoogle Scholar
[2]Gradshteyn, I. S. and Ryzhik, I. M., 1965. Tables of Integrals, Series and Products. Academic Press.Google Scholar
[3]Lowndes, J. S., 1968. ‘Some triple series equations involving Jacobi polynomials’, Proc. Edinb. Math. soc., 6, 101108.CrossRefGoogle Scholar
[4]Sneddon, I. N., 1951. Fourier Transforms. McGraw Hill.Google Scholar
[5]Sneddon, I. N., 1966. Mixed Boundary Value Problems in Potential Theory. North Holland.Google Scholar
[6]Sneddon, I. N. and Srtvastav, R. P., 1965. ‘The stress in the vicinity of an infinite row of col-linear cracks in an elastic body’, Proc. Roy. Soc. Edinb., A, 67, 3949.Google Scholar
[7]Srtvastav, R. P., 1964. ‘Dual series relations 111. Dual relations involving trigonometric series’, Proc. Roy. Soc. Edinb., A, 66, 173184.Google Scholar
[8]Srivastava, K. N., 1967. ‘On triple series equations involving series of Jacobi Polynomials’, Proc. Edinb. Math. soc., 15, 221231.CrossRefGoogle Scholar
[9]Srtvastava, K. N. and Lowengrub, M., 1970. ‘Finite Hilbert transform technique for triple integral equations with trigonometric kernels’, Proc. Roy. Soc. Edinb., A, 68, 309321.Google Scholar
[10]Tranter, C. J., 1960. ‘Some triple integral equations’, Proc. Glasg. Math. Ass., 4, 200203.CrossRefGoogle Scholar
[11]Tranter, C. J., 1969. ‘Some triple trigonometrical series’, Glasg. Math. J., 10, 121125.CrossRefGoogle Scholar