TY - EJOU
AU - Alam, N.
AU - Khan, W. A.
AU - Obeidat, S.
AU - Muhiuddin, G.
AU - Diab, N. S.
AU - Zaidi, H. N.
AU - Altaleb, A.
AU - Bachioua, L.
TI - A Note on Bell-Based Bernoulli and Euler Polynomials of Complex Variable
T2 - Computer Modeling in Engineering \& Sciences
PY - 2023
VL - 135
IS - 1
SN - 1526-1506
AB - In this article, we construct the generating functions for new families of special polynomials including two parametric kinds of Bell-based Bernoulli and Euler polynomials. Some fundamental properties of these functions are given. By using these generating functions and some identities, relations among trigonometric functions and two parametric kinds of Bell-based Bernoulli and Euler polynomials, Stirling numbers are presented. Computational formulae for these polynomials are obtained. Applying a partial derivative operator to these generating functions, some derivative formulae and finite combinatorial sums involving the aforementioned polynomials and numbers are also obtained. In addition, some remarks and observations on these polynomials are given.
KW - Bernoulli polynomials; euler polynomials; bell polynomials; stirling numbers
DO - 10.32604/cmes.2022.021418