Calculating repetitively

The Antonsen - Bormann idea was originally proposed by these authors for the computation of the heat kernel in curved space; it was also used by the author recently with the same objective but for the Lagrangian density for a real massive scalar field in 2 + 1 dimensional stationary curved space. Subsequently, it was reworked with advantage - but to determine the zeta function for the said model using the Schwinger operator expansion. The repetitive nature of that calculation at all higher orders(≥ 3) in the gravitational constant G suggests the use of the Dirac delta-function and one of its integral representations - in that it is convenient to obtain answers; in anticipation of its systematic application to all orders ≥ 3 in G and the exact evaluation of η(s) this paper illustrates in detail the evaluation of some integrals relevant to the third order calculation.