Canonical Equations and Symmetry Techniques forq-Series

Abstract

The authors introduce symmetry techniques for the classification and derivation of generating functions for families of basic hypergeometric functions, in analogy with the Lie theory techniques for ordinary hypergeometric functions. To each family of basic hypergeometric functions there is associated a canonical system of partial q-difference equations and the symmetries of these equations are used to derive q-series identities and orthogonality relations for the special functions