Four families of Weyl group orbit functions of B3 and C3

The properties of the four families of special functions of three real variables, called here C-, S-, S-s-, and S-l-functions, are studied. The S-s- and S-l-functions are considered in all details required for their exploitation in Fourier expansions of digital data, sampled on finite fragment of lattices of any density and of the 3D symmetry imposed by the weight lattices of B-3 and C-3 simple Lie algebras/groups. The continuous interpolations, which are induced by the discrete expansions, are exemplified and compared for some model functions. (C) 2013 AIP Publishing LLC.