On some integrals arising in mathematical physics

This paper presents in the first section the exact evaluation of three single integrals relating to the dielectric behavior of two-dimensional electron plasmas. In the second section we present a procedure for reducing 3d-dimensional integrals of the form: ∫∫∫dqdpdkD(q)(p+k+q)?(p)1??(p+q)]?(k)1??(k+q)], where the vectors lie in d-dimensional space and ? denotes the Fermi function, to tractable form. The second-order exchange integral for a d-dimensional electron gas is taken as an example and is evaluated in closed form as a function of d.