Cumulative STF coefficients evaluation and validation

Decomposition of geophysical functions in ranks on degrees of components of a single position vector with coefficients in the form of the indexes of tensors, symmetric and traceless on any couple (symmetric and trace free [STF] tensors or deviators), is applied along with decomposition on surface harmonics (scalar, vector, and tensor). The article considers the problem of deviator decomposition of a function having the special form of a series of degrees of components of a unit radius vector. The algorithm evaluation of STF coefficients using known values of series coefficients is under consideration. Taking into account that often only the first several of these coefficients are used, the author created and presented a table with several coefficient formulas for reference and validation. The STF-formalism is mainly used for the representation of radiative gravity fields and gravitational waves in general relativity; however, it can also be applied in mathematical physics to represent spherical harmonics, including fluid dynamics in Earth's outer core and seismic wave analysis.