G-spinors, SGTF, CGTF and HGTF

In molecular calculations it is convenient to express G-spinors in terms of Spherical Gaussian-type Functions (SGTF) [107] 

Notice that only the nonrelativistic value of the orbital angular momentum quantum number attached to the large component, appears above. 

Solid harmonics (r) are homogeneous polynomials of degree / in the coordinates 

SO that SGTF can be written as a linear combination of Cartesian Gaussian-type functions (CGTF) 

Whilst it is vital to retain the symmetry properties of SGTF in subsequent manipulations, the direct construction of expressions for the overlap densities 

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