Integrals of Lipschitz-Hankel type in analysis of magnetostatic fields

A boundary-integral model of the static magnetic field due to cylindrical permanent magnets that is put in free space is considered. Magnetic scalar potential quantities created by a virtual quantity "surface magnetic charge density" is expressed by means of Lipschitz-Hankel integrals that for the considered case are reducible (by the way of hypergeometric series) to some algebraic expressions, in which elliptic integrals of various kinds occur. This approach seems to be more effective than that can be reached by the use of a typical professional software for the field problems in which numerical integration, being not quite conform to the considered case, is common. The magnet subjected to the analysis has to be virtually subdivided in some number of elementary pieces, inside of which the uniform distribution of the inherent magnetization is supposed.