JMP Nameplate
  • Volume/Page
  • Keyword
  • DOI
  • Citation
  • Advanced
   
 
 
 

Flickr Twitter UniPHY Group iResearch App Facebook

Journal of Mathematical Physics / Volume 48 / Issue 4 / METHODS OF MATHEMATICAL PHYSICS

J. Math. Phys. 48, 043507 (2007); http://dx.doi.org/10.1063/1.2712895 (12 pages)

Closed-form summation of the Dowker and related sums

Djurdje Cvijović1 and H. M. Srivastava2

1Atomic Physics Laboratory, Vinča Institute of Nuclear Sciences, P.O. Box 522, YU-11001 Belgrade, Serbia
2Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3P4, Canada

View MapView Map

(Received 14 January 2007; accepted 6 February 2007; published online 19 April 2007)

Finite sums of powers of cosecants appear in a wide range of physical problems. We, through a unified approach which uses contour integrals and residues, establish the summation formulas for two general families of such sums. One of them is the family which was first studied and summed in closed form by Dowker [Phys. Rev. D 36, 3095 (1987)] , while the other is related to it and has not been studied before. Our summation formulas of the Dowker sums involve only the Stirling numbers of the first kind and the (ordinary) Bernoulli polynomials and numbers, unlike the earlier summation formulas in which either the higher-order Bernoulli numbers and polynomials or the multiple sums involving the Bernoulli numbers and their products, were used. A great deal of other (known or presumably new) closed-form summations follows as straightforward corollaries to these formulas. Among them are two special cases of the celebrated Verlinde’s formula and numerous sums encountered in various physical problems by McCoy and Orrick [J. Stat. Phys. 83, 839 (1996)] , Gervois and Mehta [J. Math. Phys. 36, 5098 (1995)] , and Henkel and Lacki [Phys. Lett. A 138, 105 (1989)] .

© 2007 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. PRELIMINARIES AND STATEMENT OF THE RESULTS
  3. PROOFS OF THE THEOREMS
  4. CONCLUDING REMARKS AND OBSERVATIONS

RELATED DATABASES

To view database links for this article, you need to log in.

KEYWORDS and PACS

Keywords

polynomials, number theory, integral equations

PACS

  • 02.10.De

    Algebraic structures and number theory

  • 02.30.Lt

    Sequences, series, and summability

  • 02.30.Rz

    Integral equations

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.2712895

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    J. S. Dowker, Phys. Rev. D 36, 3095 (1987).

    J. S. Dowker, J. Math. Phys. 30, 770 (1989)JMAPAQ000030000004000770000001.

    A. Gervois and M. L. Mehta, J. Math. Phys. 36, 5098 (1995)JMAPAQ000036000009005098000001.

    A. Gervois and M. L. Mehta, J. Math. Phys. 37, 4150 (1996)JMAPAQ000037000008004150000001.


For access to citing articles, you need to log in.



Close

Google Calendar

ADVERTISEMENT

Your Recent History Recent History Help

Recently Viewed

  1. Closed-form summation of the Dowker and related sums
  2. MHD α2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
  3. On the Casimir of the group ISL(n,R) and its algebraic decomposition
  4. “Squashed entanglement”: An additive entanglement measure
  5. A central extension of Uq sl(2∣2)(1) and R-matrices with a new parameter
Go to AIP Home
Copyright © American Institute of Physics
close