Evaluation of a class of Feynman diagrams for all numbers of loops and dimensions

Abstract A simple formula is derived for the l-loop member of a class of massless, dimensionally regularized Feynman diagrams, using a recursive algorithm based on the method of integration by parts of Chetyrkin and Tkachov. The result has been verified by explicit computation up to 25 loops. In four dimensions one obtains I l = (2l)!ζ(2l − 1) (l!) 2 , the values I2 = 6ζ(3) and I3 = 20ζ(5) giving the most difficult diagrams encountered in two- and three-loop calculations.