Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-05-13T13:34:20.868Z Has data issue: false hasContentIssue false
  • English
  • Français

Some formulas related to dilogarithms, the zeta function and the Andrews-Gordon identities

Published online by Cambridge University Press:  09 April 2009

Bruce Richmond  and
George Szekeres
Bruce Richmond
Affiliation:
University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
George Szekeres
Affiliation:
University of New South Wales, Kensington, N.S.W. 2033, Australia
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.

It is shown that non-trivial relations between certain values of the dilogarithm function can be obtained through the asymptotic comparison of coefficients of the expressions which appear in the Rogers-Ramanujan and Andrews-Gordon identities.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 3 , October 1981 , pp. 362 - 373
Copyright
Copyright © Australian Mathematical Society 1981

References

Abel, N. H. (1839), Oeuvres Complètes, vol. 2 (Gröndahl).Google Scholar
Abramowitz, Milton and Stegun, Irene A. (1964), Handbook of mathematical functions (National Bureau of Standards).Google Scholar
Andrews, George E. (1976), The theory of partitions (Encyclopedia of Mathematics and its Applications, vol. 2, Addison-Wesley).Google Scholar
Lewin, L. (1958), Dilogarithms (Macdonald, London).Google Scholar
Richmond, B. and Szekeres, G. (1978), ‘The Taylor coefficients of certain infinite products’, Acta Sci. Math. 40, 347–369.Google Scholar
Szekeres, G. (1953), ‘Some asymptotic formulae in the theory of partitions II’, Quart. J. Math. Oxford Ser. 4, 96–111.CrossRefGoogle Scholar
Watson, G. N. (1937), ‘A note on Spence's logarithmic transcendant’, Quart. J. Math. Oxford Ser. 8, 39–42.CrossRefGoogle Scholar