Hostname: page-component-6d856f89d9-76ns8 Total loading time: 0 Render date: 2024-07-16T07:38:46.097Z Has data issue: false hasContentIssue false
  • English
  • Français

On improper integrals of products of logarithmic, power and Bessel functions

Published online by Cambridge University Press:  17 April 2009

M. Aslam Chaudhry  and
M. Ahmad
M. Aslam Chaudhry
Affiliation:
Department of Mathematical SciencesKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia
M. Ahmad
Affiliation:
Department of Mathematical SciencesKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we have evaluated the integral . A new integral representation of the Euler constant is shown. Some special cases of the result are discussed and an open problem is posed.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 3 , June 1992 , pp. 395 - 398
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Askey, R., Koornwinder, T.H. and Rahman, M., ‘An integral of products of ultraspherical functions and a q−extension’, J. London Math. Soc. 33, 133–148.Google Scholar
[2]Bailey, W.N., ‘Some infinite integrals involving Bessel functions’, Proc. London math. Soc. 40 (1936), 37–48.CrossRefGoogle Scholar
[3]Budak, B.M., Fomin, S.V., Multiple integrals, field theory and series (Mir Publishers, 1978).Google Scholar
[4]Erdelyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F.G., Integral transforms, Vol. I (McGRaw-Hill, 1954).Google Scholar
[5]Gradshteyn, I.S. and Ryzhik, I.M., Tables of integrals, series and products (Academic Press, 1980).Google Scholar
[6]Lebedev, N.N., Special functions and their applications (Dover Publications Inc., 1972).Google Scholar
[7]Watson, G.N., Theory of Bessel functions, 2nd edition (Cambridge University Press, 1944).Google Scholar