Extremely compact formulae for auxiliary functions and integralsof some molecular magnetic tensors integrals over Slater Type Basis Functions: K n(r), T rs(r) ,mi and ki integrals.

We presented in previous work the methodology used to calculate the integrals appeared when an atom or a molecule is subject to magnetic fields of different origin, that can be an external homogenous field and that created by the nuclear magnetic moment. These integrals are rigorously and analytically evaluated for Slater Type nsnp basis Functions using spherical polar coordinates with the nucleus as origin or elliptic coordinates.Properties of the Levi-Civita tensor of rank 3 , gamma functions, properties of rotation matrix and symmetry properties of field-independent atomic orbitals have permitted to obtain a very condense formalism. We give here very compact formulae for all auxiliary functions and integrals which are needed to obtain final formulas that can be used in a FORTRAN program.