<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The aim of this note is to study the distribution function of certain sequences of positive integers, including, for example, Bell numbers, factorials and primorials. In fact, we establish some general asymptotic formulas in this regard. We also prove some limits that connect these sequences with the number <italic>e</italic>. Furthermore, we present a generalization of the primorial.</p></abstract>

The aim of this note is to study the distribution function of certain sequences of positive integers, including, for example, Bell numbers, factorials and primorials. In fact, we establish some general asymptotic formulas in this regard. We also prove some limits that connect these sequences with the number e. Furthermore, we present a generalization of the primorial.

A Note on the Asymptotic Behavior of the Distribution Function of a General Sequence

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

The aim of this note is to study the distribution function of certain sequences of positive integers, including, for example, Bell numbers, factorials and...

A Note on the Asymptotic Behavior of the Distribution Function of a General Sequence

Published Online: Jan 26, 2021

Page range: 44 - 54

Received: Jun 14, 2020

Accepted: Dec 29, 2020

DOI: https://doi.org/10.2478/amsil-2020-0027

Keywords
Bell numbers, factorials, primorials, distribution function, asymptotic behavior, the number

© 2021 Reza Farhadian et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

A Note on the Asymptotic Behavior of the Distribution Function of a General Sequence

Published Online: Jan 26, 2021

Page range: 44 - 54

Received: Jun 14, 2020

Accepted: Dec 29, 2020

DOI: https://doi.org/10.2478/amsil-2020-0027

KeywordsBell numbers, factorials, primorials, distribution function, asymptotic behavior, the number

© 2021 Reza Farhadian et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Bell numbers, factorials, primorials, distribution function, asymptotic behavior, the number