Algebraic Table of Vector-Addition Coefficients forj2=52

Abstract

Vector-addition coefficients are given by a terminating hypergeometric sum of the ${}_3{}^{}{}_{}{}^{}F_2^{}{}_{}{}^{}$ type, which is easily converted to a simplified form. This form is equivalent to those found independently by Gaunt, van der Waerden, and Racah. It is used to fill the gap for $j_2=\frac{5}{2}$ in the literature of published algebraic tables.