An algebraic interpretation of the continuous big q-Hermite polynomials

Abstract

The continuous big $q$-Hermite polynomials are shown to realize a basis for a representation space of an extended $q$-oscillator algebra. An expansion formula is algebraically derived using this model.

Cited by in corpus (2)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• New connection formulae for some q-orthogonal polynomials in q-Askey scheme