Non-standard orthogonality for the little -Laguerre polynomials

Little q -Laguerre polynomials { p n ( ⋅ ; a | q ) } n = 0 ∞ are classically defined for 0 < q < 1 and 0 < a q < 1 . After extending this family to a new one in which arbitrary real values of the parameter a are allowed, we give an orthogonality condition for those cases for which Favard’s Theorem fails to work.