Functiones et Approximatio Commentarii Mathematici

On extended Eulerian numbers

Abdelmejid Bayad, Mohand Ouamar Hernane, and Alain Togbé

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Abstract

In this paper, we will study some properties of the extended Eulerian numbers $H(n,\lambda)$, with a parameter $\lambda$. In fact, for any integer $n$, we investigate the asymptotic behavior, find lower and upper bounds for $H(n,\lambda)$. As application, for a champion number $N$, we obtain asymptotic formulas, lower and upper bounds of the arithmetic functions $\omega(N)$ and $\Omega(N)$.

Article information

Source
Funct. Approx. Comment. Math. Volume 55, Number 1 (2016), 113-130.

Dates
First available in Project Euclid: 19 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.facm/1474301233

Digital Object Identifier
doi:10.7169/facm/2016.55.1.8

Mathematical Reviews number (MathSciNet)
MR3549016

Subjects
Primary: 11A25: Arithmetic functions; related numbers; inversion formulas
Secondary: 11N37: Asymptotic results on arithmetic functions 49K10: Free problems in two or more independent variables

Keywords
Kalmar's function extended Eulerian numbers Champion numbers asymptotic formula Ikehara-Wiener theorem

Citation

Bayad, Abdelmejid; Hernane, Mohand Ouamar; Togbé, Alain. On extended Eulerian numbers. Funct. Approx. Comment. Math. 55 (2016), no. 1, 113--130. doi:10.7169/facm/2016.55.1.8. https://projecteuclid.org/euclid.facm/1474301233


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