Abstract. Following Dirac, Schwartz, and others, distributions are well understood (and widely used in physics) as 'generalized functions'. However, a function with a nonintegrable singularity does not define a distribution automatically or unambiguously. We review a variety of ways in which such distributions can be defined, sometimes with inequivalent results, or results containing arbitrary constants. We give special attention to the function cosech² x and its semiclassical scaling limit, which have recently attracted some attention in statistical mechanics.

PACS numbers: 02.30.−f, 03.70.+k, 11.10.−z

A corrigendum for this article has been published in 2005 J. Phys. A: Math. Gen. 38 7785

Print publication: Issue 13 (5 April 2002)
Received 29 September 2001, in final form 2 January 2002
Published 22 March 2002