We use WZ-summation methods to compute recurrences for the Ising-class integrals Cn,k. In this context, we describe an algorithmic approach to obtain homogeneous and inhomogeneous recurrences for a general class of multiple contour integrals of Barnes’ type.

Explicit formulae for Weber-Schafheitlin type integrals with exponent 1 are derived. The results of these integrals are distributions on R+. Received 07 April 2008; Revised 30 June 2008

Some principal value integrals of Glauert’s type are calculated analytically. These integrals appear when dealing with the hydrodynamic impact problem of a two-dimensional wedge onto a liquid free surface in the potential theory. © 2004 Elsevier Ltd. All rights reserved.