Unified BernoulliEuler polynomials of Apostol type
Abstract
The object of this paper is to introduce and study properties of unified ApostolBernoulli and ApostolEuler polynomials noted by $\left\{\mathfrak{V_{n}}(x;\lambda;\mu)\right\}_{n \geq 0}$. We study some arithmetic properties of $\left\{\mathfrak{V_{n}}(x;\lambda;\mu)\right\}_{n \geq 0}$ as their connection to ApostolEuler polynomials and ApostolBernoulli polynomials. Also, we give derivation and integration representations of $\left\{\mathfrak{V_{n}}(x;\lambda;\mu)\right\}_{n \geq 0}$. Finally, we use the umbral calculus approach to deduce symmetric identities.
 Publication:

arXiv eprints
 Pub Date:
 January 2021
 arXiv:
 arXiv:2102.00137
 Bibcode:
 2021arXiv210200137B
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Number Theory;
 11B68;
 11B83;
 11C08;
 11C20