Some comments on the application of analytic regularisation to the Casimir forces

Abstract

Expressing the generalised zeta function Sigma n omega n-s in terms of the 'partition function' Sigma ne- alpha omega (n), alpha the authors show in this paper why they obtain the same answer for for the Casimir effect (in many physical situations) if they use, alternatively, the analytic continuation procedure for the zeta function or take the first derivative of the above partition function and make alpha to 0+ with the neglect of all pole terms in alpha =O.