Two q-operational equations and Hahn polynomials
Abstract
Motivated by Liu's recent work in Liu2022. We shall reveal the essential feature of Hahn polynomials by presenting two new q-exponential operators. These lead us to use a systematic method to study identities involving Hahn polynomials. As applications, we use the method of q-exponential operator to prove the bilinear generating function of Hahn polynomials and Heine's second transformation formula. Moreover, a generalization of q-Gaussian summation is given, too.
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