q-Taylor and interpolation series for Jackson q-difference operators

We prove q-Taylor series for Jackson q-difference operators. Absolute and uniform convergence to the original function are proved for analytic functions.We derive interpolation results for entire functions of q-exponential growth which is less than ln q −1, 0 < q <1, from its values at the nodes {aq −n, n ∈ N}, a is a non-zero complex number with absolute and uniform convergence criteria. © 2008 Elsevier Inc. All rights reserved.