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$q$-Addition theorems for the $q$-Appell polynomials and the associated classes of $q$-polynomials expansions

Patrick Njionou Sadjang
대한수학회 (The Korean Mathematical Society)|2018.09|대한수학회지 (Journal of the KMS)|제55권 제5호|pp. 1179-1192

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참고문헌

키워드

generating functions$q$-addition theorem$q$-Appell polynomials$q$-Bernoulli$q$-Euler and $q$-Genocchi polynomials$q$-orthogonal polynomials
주제분류수학

초록

Several addition formulas for a general class of $q$-Appell sequences are proved. The $q$-addition formulas, which are derived, involved not only the generalized $q$-Bernoulli, the generalized $q$-Euler and the generalized $q$-Genocchi polynomials, but also the $q$-Stirling numbers of the second kind and several general families of hypergeometric polynomials. Some $q$-umbral calculus generalizations of the addition formulas are also investigated.

Abstract

Several addition formulas for a general class of $q$-Appell sequences are proved. The $q$-addition formulas, which are derived, involved not only the generalized $q$-Bernoulli, the generalized $q$-Euler and the generalized $q$-Genocchi polynomials, but also the $q$-Stirling numbers of the second kind and several general families of hypergeometric polynomials. Some $q$-umbral calculus generalizations of the addition formulas are also investigated.

참고문헌 (21)

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