Apostol-Bernoulli functions, derivative polynomials and Eulerian polynomials

Abstract

This is a short survey of a class of functions introduces by Tom Apostol. The survey is focused on their relation to Eulerian polynomials, derivative polynomials, and also on some integral representations.

Cited by in corpus (11)

• Geometric Polynomials: Properties and Applications to Series with Zeta Values
• Combinatorial identities associated with new families of the numbers and polynomials and their approximation values
• Polynomials with r-Lah coefficient and hyperharmonic numbers
• Some formulae for products of Fubini polynomials with applications
• On some expansions for the Euler Gamma function and the Riemann Zeta function
• Derivation of Computational Formulas for certain class of finite sums: Approach to Generating functions arising from $p$-adic integrals and special functions
• Novel Formulas for B-Splines, Bernstein Basis Functions and special numbers: Approach to Derivative and Functional Equations of Generating Functions
• Two closed forms for the Apostol-Bernoulli polynomials
• A new Generating Function of Exponential Polynomials and its Applications to the Related Polynomials and Numbers
• New results on p-Bernoulli numbers
• On the Taylor Coefficients of the Hurwitz Zeta Function