On Harmonic Geometric Polynomials and Numbers


Kargın L.

33èmes Journées Arithmétiques, Luxembourg, Luxembourg, 30 June - 04 July 2025, pp.46, (Summary Text)

  • Publication Type: Conference Paper / Summary Text
  • City: Luxembourg
  • Country: Luxembourg
  • Page Numbers: pp.46
  • Akdeniz University Affiliated: Yes

Abstract

We obtain new recurrence relations, explicit formulas, and convolution identities for harmonic geometric polynomials $H w_n(x)$ defined by

\[

H w_n(x)=\sum_{k=1}^{n}

\left\{\begin{matrix}

n\\

k

\end{matrix}\right\}

k!H_k x^k,

\]

where

\[

\left\{\begin{matrix}

n\\

k

\end{matrix}\right\}

\]

denotes the Stirling number of the second kind and $H_n$ is the $n$th harmonic number. Moreover, we relate these polynomials to Bernoulli and Euler numbers, and through these relations, we obtain new explicit representations and recurrence relations for Bernoulli and Euler numbers.