Quasibinomial Representations of Clebsch-Gordan Coefficients. II. ``Negative'' Representations
S. M. Razaullah Ansari
Abstract
S. M. Razaullah Ansari
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.
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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.
Key concepts: Clebsch–Gordan coefficients, Symbol (formal), Mathematics, Irreducible representation, Pure mathematics, Representation (politics), Algebra over a field, Construct (python library)