Evaluation of Watson-like integrals for a hyper bcc antiferromagnetic lattice

Watson-like integrals for a d-dimensional bcc antiferromagnetic lattice are evaluated in an exact way in terms of generalized hypergeometric functions. A simple formula connecting Id and Jd+1 is given along with the differential equations for Id(η) and Jd(η). An application of Id and Jd in the theory of the Heisenberg antiferromagnet is discussed, together with possible generalizations to non-integer values of d. Corresponding integrals for sc lattices are also briefly reviewed.