A note on the asymptotic behavior of the distribution function of a general sequence

Reza Farhadian; Rafael Jakimczuk

Published: 2021-01-26
Language: EN

Vol. 35 No. 1 (2021)

A note on the asymptotic behavior of the distribution function of a general sequence

Reza Farhadian

, Rafael Jakimczuk

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.

(EN)

Keywords:

Bell numbers , factorials , primorials , distribution function , asymptotic behavior , the number e (EN)

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Farhadian, R., & Jakimczuk, R. (2021). A note on the asymptotic behavior of the distribution function of a general sequence. Annales Mathematicae Silesianae, 35(1), 44–54. Retrieved from https://trrest.vot.pl/ojsus/index.php/AMSIL/article/view/13473

References

1. M. Abramowitz and I.A. Stegun (eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications, New York, 1972.
2. G.E. Andrews, The Theory of Partitions, Cambridge University Press, Cambridge, 1984.
3. E.T. Bell, Exponential numbers, Amer. Math. Monthly 41 (1934), no. 7, 411–419.
4. E.T. Bell, Exponential polynomials, Ann. of Math. (2) 35 (1934), no. 2, 258–277.
5. N.G. de Bruijn, Asymptotic Methods in Analysis, Dover Publications, New York, 1981.
6. R. Farhadian and R. Jakimczuk, Notes on a general sequence, Ann. Math. Sil. 34 (2020), no. 2, 193–202.
7. R. Jakimczuk, An observation on the Cipolla’s expansion, Mathematical Sciences. Quarterly Journal 2 (2008), no. 2, 219–222.
8. R. Jakimczuk, Functions of slow increase and integer sequences, J. Integer Seq. 13 (2010), no. 1, Article 10.1.1, 14 pp.
9. R. Jakimczuk, Integer sequences, functions of slow increase, and the Bell numbers, J. Integer Seq. 14 (2011), no. 5, Article 11.5.8, 11 pp.
10. J. Rey Pastor, P. Pi Calleja, and C.A. Trejo, Análisis Matemático, Vol. 1, Editorial Kapelusz, Buenos Aires, 1969. Google Scholar

Reza Farhadian

farhadian.reza@yahoo.com
https://orcid.org/0000-0003-4027-9838

Affiliation:

Department of Statistics, Razi University, Iran Iran, Islamic Republic of

Rafael Jakimczuk

Affiliation:

División Matemática, Universidad Nacional de Luján, República Argentina Argentina

Vol. 35 No. 1 (2021)
Published: 2021-02-10

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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