On Harmonic Geometric Polynomials and Numbers
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.