ON THREE INTEGRALS ARISING IN THE THEORY OF ANISOTROPIC CRITICALITY

Three integrals encountered in earlier studies of anisotropic criticality (anisotropic dispersion laws characterised by the coupling constant f) are solved in terms of elementary functions. The nature of the singularity for the case f→1 which corresponds to an effectively reduced dimensionality has been revealed. Double power-series representations for the integrals are also found and some mathematical implications and by-products are discussed. The advance relates to a prospective full-scope analysis of dipolar criticality.