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

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Abstract

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 lnq−1, 0<q<1, from its values at the nodes {aqn,nN}, a is a non-zero complex number with absolute and uniform convergence criteria.

Keywords

q-Taylor series
Jackson q-difference operator

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This research is supported by Alexander von Humboldt foundation under the number 3.4-AGY/1039259.