General Limit Formulae Involving Prime Numbers

• Autorzy: Reza Farhadian , Rafael Jakimczuk
• Języki publikacji: EN

Abstrakty

EN

Let p_n be the nth prime number. In this note, we study strictly increasing sequences of positive integers A_n such that the limit lim_{n→∞}(A_1A_2···A_n)^{1/p_n} = e holds. This limit formula is in fact a generalization of some previously known results. Furthermore, some other generalizations are established.(original abstract)

Słowa kluczowe

EN

Mathematics; Functions

PL

Matematyka; Funkcje

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2022
• Tom: 36 (2)
• Strony: 176--183

Twórcy

autor

Reza Farhadian

• Razi University Kermanshah, Iran

autor

Rafael Jakimczuk

• National University of Luján, Argentina

Bibliografia

• Farhadian R., A remark on lim_{n→∞}\sqrt[p_n]{p_1p_2···p_n} = e, Math. Gaz. 105 (2021), 311-312.
• Farhadian R., A generalization of Euler's limit, Amer. Math. Monthly 129 (2022), 384.
• Farhadian R. and Jakimczuk R., Notes on a general sequence, Ann. Math. Sil. 34 (2020), 193-202.
• Farhadian R. and Jakimczuk R., A note on the geometric mean of prime numbers and generalizations, J. Discrete Math. Sci. Cryptogr. (2020). DOI: 10.1080/09720529.2020.1723920
• Farhadian R. and Jakimczuk R., A note on two fundamental recursive sequences, Ann. Math. Sil. 35 (2021), 172-183.
• Farhadian R. and Jakimczuk R., A further generalization of lim_{n→∞}\sqrt[n]{n!}/n = 1/e, Ann. Math. Sil. (2022). DOI: 10.2478/amsil-2022-0006
• Farhadian R. and Jakimczuk R., On a sequence involving products of primes, J. Interdiscip. Math. (2022). DOI: 10.1080/09720502.2021.1961981
• Finch S.R., Mathematical Constants, Cambridge University Press, Cambridge, 2003.
• Jakimczuk R., The ratio between the average factor in a product and the last factor, Math. Sci. Q. J. 1 (2007), 53-62.
• Jakimczuk R., Functions of slow increase and integer sequences, J. Integer Seq. 13 (2010), Article 10.1.1, 14 pp.
• Rey Pastor J., Pi Calleja P., and Trejo C.A., Análisis Matemático, Vol. 1, Editorial Kapelusz, Buenos Aires, 1969.

Identyfikatory

DOI

10.2478/amsil-2022-0014