Addition formulas for q-special functions

Research paper by Erik Koelink

Indexed on: 14 Jun '95Published on: 14 Jun '95Published in: Mathematics - Quantum Algebra


A general addition formula for a two-parameter family of Askey-Wilson polynomials is derived from the quantum $SU(2)$ group theoretic interpretation. This formula contains most of the previously known addition formulas for $q$-Legendre polynomials as special or limiting cases. A survey of the literature on addition formulas for $q$-special functions using quantum groups and quantum algebras is given.