Quasibinomial Representations of Clebsch-Gordan Coefficients. II. ``Negative'' Representations

Abstract

New quasibinomial forms are derived from the quasibinomial forms given previously by making use of both positive and negative generalized powers. They turn out to be a new representation of the Wigner‐type unsymmetrical formulas of Clebsch‐Gordan coefficients for angular momenta. Consequently, formulas of Racah, Majumdar, and Shimpuku are deduced as special cases. Rules to construct a square symbol are given from which all these ``negative'' quasibinomial representations or, more precisely, expansions can be read off directly. Thus, a unified treatment of both symmetrical and unsymmetrical formulas of Clebsch‐Gordan coefficients is thereby accomplished.