Two q-Operational Equations and Hahn Polynomials
Copyright policy )Two q-Operational Equations and Hahn Polynomials
Motivated by Liu's recent work in \cite{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.
- East China Normal University China (People's Republic of)
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), basic hypergeometric series, \(q\)-derivative, \(q\)-operational equation, Hahn polynomials, Mathematics - Classical Analysis and ODEs, \(q\)-calculus and related topics, \(q\)-Gauss summation, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 05A30, 33D90, Applications of basic hypergeometric functions
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), basic hypergeometric series, \(q\)-derivative, \(q\)-operational equation, Hahn polynomials, Mathematics - Classical Analysis and ODEs, \(q\)-calculus and related topics, \(q\)-Gauss summation, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 05A30, 33D90, Applications of basic hypergeometric functions
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