On Harmonic Geometric Polynomials and Numbers


Kargın L.

33èmes Journées Arithmétiques, Luxembourg, Lüksemburg, 30 Haziran - 04 Temmuz 2025, ss.46, (Özet Bildiri)

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: Luxembourg
  • Basıldığı Ülke: Lüksemburg
  • Sayfa Sayıları: ss.46
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.