Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-20T16:19:50.751Z Has data issue: false hasContentIssue false
  • English
  • Français

XIV.—Dual Series Relations. I. Dual Relations Involving Fourier-Bessel Series*

Published online by Cambridge University Press:  14 February 2012

I. N. Sneddon  and
R. P. Srivastav
Get access Rights & Permissions [Opens in a new window]

Synopsis

The solution of the dual series relations

where {λn) is the sequence of positive zeros of the Bessel function Jν(αλ), arranged in order of increasing magnitude, þ and ν are real numbers (−1 <þ < 1, ν >0), the functions, f1(ρ), f2(ρ) being prescribed, is obtained by giving an integral representation of {αn} in terms of a single function g(t). The problem is reduced to that of solving a Fredholm integral equation of the second kind for the auxiliary function g(t).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 66 , Issue 3 , 1963 , pp. 150 - 160
Copyright
Copyright © Royal Society of Edinburgh 1963

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

Cooke, J. C., and Tranter, C. J., 1959. “Dual Fourier-Bessel Series”, Quart. J. Meek., 12, 379–385.Google Scholar
Erdelyi, A. (Ed.), 1954. Tables of Integral Transforms. New York, London: McGraw-Hill.Google Scholar
Sneddon, I. N., 1962a. “Note on an electrified circular disk situated inside a coaxial infinite hollow cylinder.” Proc. Camb. Phil. Soc., 58, 621–624.CrossRefGoogle Scholar
Sneddon, I. N., 1962b. “Fractional Integration and Dual Integral Equations.” N. C. St Coll. Appl. Math. Res. Group Rep., PSR-6.CrossRefGoogle Scholar
Watson, G. N., 1944. A Treatise on the Theory of Bessel Functions, 2nd Edn. Cambridge University Press.Google Scholar