Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-26T01:42:36.940Z Has data issue: false hasContentIssue false
  • English
  • Français

XXIII.— Dual Series Relations.* V. A Generalized Schlömilch Series and the Uniqueness of the Solution of Dual Equations 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
Get access Rights & Permissions [Opens in a new window]

Synopsis

The methods employed in papers I–IV of this series are modified to provide the solution of certain dual equations involving trigonometric series. It is necessary to introduce a modified form of the conventional operators of fractional integration and to discuss their relation with generalized Schlömilch series expansions of an arbitrary function. These general methods are illustrated by detailed reference to a particular special case.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 66 , Issue 4 , 1964 , pp. 258 - 268
Copyright
Copyright © Royal Society of Edinburgh 1964

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

References to Literature

Erdélyi, A. (Ed.), 1954. Tables of Integral Transforms. New York, London: McGraw-Hill.Google Scholar
Sneddon, I. N., 1961. “Crack Problems in the Mathematical Theory of Elasticity”, N.C. St Coll. Engng. Res. Dep. Rep., 126/1.Google Scholar
Sneddon, I. N., 1962. “Fractional Integration and Dual Integral Equations”, N.C. St Col. Appl. Math. Res. Group Rep., PSR-6.CrossRefGoogle Scholar
Sneddon, I. N., and Srivastav, R. P., 1965. “The Stress in the Vicinity of an Infinite Row of Collinear Cracks in an Elastic Body”, Proc. Roy. Soc. Edin., A, 67. [In the press.]CrossRefGoogle Scholar
Srivastav, R. P., 1963. “A note on certain integral equations of Abel-type”, Proc. Edin. Math. Soc, 13, 271–272.CrossRefGoogle Scholar
Srivastav, R. P., 1964. “Dual Series Relations—III. Dual Relations involving Trigonometric Series”, Proc. Roy. Soc. Edin., A, 66, 173–184.Google Scholar
Tait, R. J., 1962. Some Problems in the Mathematical Theory of Elasticity”. Ph.D. Thesis, Glasgow University.Google Scholar
Tranter, C. J., 1959. “Dual Trigonometric Series”, Proc. Glasg. Math. Ass., 4, 49–57.CrossRefGoogle Scholar
Tranter, C. J., 1960. “A Further Note on Dual Trigonometric Series”, Proc. Glasg. Math. Ass., 4, 198–200.CrossRefGoogle Scholar
Watson, G. N., 1944. A Treatise on the Theory of Bessel Functions, 2nd Edn. Cambridge University Press.Google Scholar