Geometric Polynomials: Properties and Applications to Series with Zeta Values

Abstract

We provide several properties of the geometric polynomials discussed in earlier works of the authors. Further, the geometric polynomials are used to obtain a closed form evaluation of certain series involving Riemann's zeta function.

arXiv comment18 pages

References in corpus (3)

• Apostol-Bernoulli functions, derivative polynomials and Eulerian polynomials
• Polynomials Related to Harmonic Numbers and Evaluation of Harmonic Number Series I
• Series Transformation Formulas of Euler Type, Hadamard Product of Functions, and Harmonic Number Identities

Cited by in corpus (6)

• Polynomials with r-Lah coefficient and hyperharmonic numbers
• Higher order generalized geometric polynomials
• A closed formula for the generating function of p-Bernoulli numbers
• New identities with Stirling, hyperharmonic, and derangement numbers, Bernoulli and Euler polynomials, powers, and factorials
• Sums of powers and special polynomials
• A Second Type Of Higher Order Generalised Geometric Polynomials and Higher Order Generalised Euler Polynomials