2012/01/04 by Piotr Multarzyński, Multarzyński, Piotr
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Mathematical functions and polynomials #Quantum Algebra (math.QA) #math.QA
paper · pdf · doi:10.48550/arxiv.1201.1026
arXiv admin note: text overlap with arXiv:1012.2611
arxiv created 2012/01/04 · openalex publication_date 2012/01/04 · arxiv updated 2012/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The concept of polynomials in the sense of algebraic analysis, for a single right invertible linear operator, was introduced and studied originally by D. Przeworska-Rolewicz \citeDPR. One of the elegant results corresponding with that notion is a purely algebraic version of the Taylor formula, being a generalization of its usual counterpart, well known for functions of one variable. In quantum calculus there are some specific discrete derivations analyzed, which are right invertible linear operators \citekac. Hence, with such quantum derivations one can associate the corresponding concept of algebraic polynomials and consequently the quantum calculus version of Taylor formula \citeMULT2. In the present paper we define and analyze, in the sense of algebraic analysis, polynomials corresponding with a given family of right invertible operators. Within this approach we generalize the usual polynomials of several variables.