We establish two new q-analogues of a Taylor series expansion for polynomials using special Askey-Wilson polynomial bases. Combining these expansions with an earlier expansion theorem we derive inverse relations and evaluate certain linearization coefficients. Byproducts include new summation theorems, new results on a q-exponential function, and quadratic transformations for q-series.
Bibliographical noteFunding Information:
Part of this work was done while the authors were visiting the Liu Bie Ju Center of Mathematical Sciences of City University of Hong Kong and they gratefully acknowledge the financial support and the hospitality of the City University of Hong Kong.
- Askey-Wilson operators
- Connection relations
- Polynomial bases
- Summation theorems
- q-exponential function