Recently, Kim-Kim [10] have studied type 2-Changhee and Daehee polynomials. They also introduced the 2-Bernoulli polynomials in order to express central factorial numbers of second kind by making use negative integral orders. Inspired their work, we consider a new class generating functions We give some identities for these including 2-Euler Stirling kind.

In this paper, we consider Bell-based Stirling polynomials of the second kind and derive some useful relations properties including summation formulas related to Bell numbers kind. Then, introduce Bernoulli order α investigate multifarious correlations derivative properties. Also, acquire diverse implicit symmetric identities for α. Moreover, attain several interesting arising from umbral calcu...

and Applied Analysis 3 2. Symmetry of Power Sum and the Generalized Bernoulli Polynomials Let χ be the Dirichlet character with conductor d ∈ N. From 1.3 , we note that ∫ X χ x edx t ∑d−1 i 0 χ i e it edt − 1 ∞ ∑ n 0 Bn,χ t n! , 2.1 where Bn,χ x are the nth generalized Bernoulli numbers attached to χ. Now, we also see that the generalized Bernoulli polynomials attached to χ are given by ∫ X χ (...

The Arakawa-Kaneko zeta functions interpolate the poly-Bernoulli numbers at the negative integers and their values at positive integers are connected to multiple zeta values. We give everywhere-convergent series expansions of these functions in terms of Bernoulli polynomials and Dirichlet series related to harmonic numbers, exhibiting their explicit analytic continuation. Differentiating the Ba...

The main aim of this paper is to introduce and investigate the degenerate type 2-unified Apostol–Bernoulli, Euler Genocchi polynomials by using monomiality principle operational methods. We give explicit relations some identities for polynomials.