The foundation for the quantum theory of angular momentum,
as an integral part of quantum mechanics, was laid in the
1920's which whitnessed profound theoretical developments.
For the atomic, molecular and nuclear physicist, the quantum
theory of angular momentum is an indispensable and essential
discipline. The discovery of new symmetries of the
Clebsch-Gordan and Racah coefficients, overlooked in the
course of time, provided the impetus to congently present
the intimate connection between angular-momentum
coefficients and the theory of generalized hypergeometric
functions.
Throughout this monograph, emphasis is placed on a good
exposition of any aspect of the theory in order to be
reliablewith respect to notations, phase factors and
numerical factors. The monograph also provides complete
solutions to some of the major problems of angular-momentum
quantum theory. The topics selected cover: Connection
between angular-momentum coefficient, relation between
angular-momentum coefficients and orthogonal polynomial,
plynomial zeros of angular-momentum coefficients, numerical
algorithms for the generation of polynomial zeros and the
computation of angular-momentum coefficients based on sets
of generalized hypergeometric functions, and
q-generalizations of angular-momentum coefficients.