Open AccessSome recurrence formulas for the q-Bernoulli and q-Euler polynomials
Author(s) -
Paçin Dere Rahime
Publication year - 2020
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2002663d
Subject(s) - mathematics , difference polynomials , bernoulli polynomials , operator (biology) , orthogonal polynomials , wilson polynomials , classical orthogonal polynomials , recurrence relation , discrete orthogonal polynomials , macdonald polynomials , algebra over a field , hahn polynomials , euler's formula , pure mathematics , gegenbauer polynomials , discrete mathematics , combinatorics , mathematical analysis , biochemistry , chemistry , repressor , transcription factor , gene
The recurrence relations have a very important place for the special polynomials such as q-Appell polynomials. In this paper, we give some recurrence formulas that allow us a better understanding of q-Appell polynomials. We investigate the q-Bernoulli polynomials and q-Euler polynomials, which are q-Appell polynomials, and we obtain their recurrence formulas by using the methods of the q-umbral calculus and the quantum calculus. Our methods include some operators which are quite handy for obtaining relations for the q-Appell polynomials. Especially, some applications of q-derivative operator are used in this work.