On certain generalized \(q\)-Appell polynomial expansions. (English) Zbl 1308.05021
Summary: We study \(q\)-analogues of three Appell polynomials, the \(H\)-polynomials, the Apostol-Bernoulli and Apostol-Euler polynomials, whereby two new \(q\)-difference operators and the NOVA \(q\)-addition play key roles. The definitions of the new polynomials are by the generating function; like in our book, two forms, NWA and JHC are always given together with tables, symmetry relations and recurrence formulas. It is shown that the complementary argument theorems can be extended to the new polynomials as well as to some related polynomials. In order to find a certain formula, we introduce a \(q\)-logarithm. We conclude with a brief discussion of multiple \(q\)-Appell polynomials.
MSC:
| 05A30 | \(q\)-calculus and related topics |
| 11B68 | Bernoulli and Euler numbers and polynomials |
| 05A10 | Factorials, binomial coefficients, combinatorial functions |
Keywords:
\(q\)-Apostol-Bernoulli polynomials; \(q\)-Apostol-Euler polynomials; \(q\)-H-polynomials; complementary argument theorem; generating function; multiple \(q\)-Appell polynomialsReferences:
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