Hostname: page-component-6bf8c574d5-mggfc Total loading time: 0 Render date: 2025-02-18T00:23:42.094Z Has data issue: false hasContentIssue false
  • English
  • Français

A generalisation of the summation formula of Plana

Published online by Cambridge University Press:  17 April 2009

Clément Frappier
Clément Frappier
Affiliation:
Département de Mathématiques et de génie industriel, École Polytechnique, C.P. 6079 Succ. Centre-Ville, Montréal (P.Q.), Canada H3C 3A7 e-mail: [email protected]
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.

An extension of the classical summation formula of Plana is obtained. The extension is obtained by using the zeros of a Bessel function of the first kind.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 2 , April 1999 , pp. 315 - 322
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Apostol, T.M., Introduction to analytic number theory (Springer-Verlag, Berlin, Heidelberg, New York, 1976).Google Scholar
[2]Ghanem, R. Ben and Frappier, C., ‘Explicit quadrature formulae for entire functions of exponential type’, J. Approx. Theory 92 (1998), 267–279.CrossRefGoogle Scholar
[3]Frappier, C. and Olivier, P., ‘A quadrature formula involving zeros of Bessel functions’, Math. Comp. 60 (1993), 303–316.CrossRefGoogle Scholar
[4]Henrici, P., Applied and computational complex analysis Vol. 1 and 2 (John Wiley and Sons, New York, 1988 and 1991).Google Scholar
[5]Watson, G.N., A treatise on the theory of Bessel functions, (2nd edition) (Cambridge University Press, Cambridge, 1952).Google Scholar