关于一般序列的注记

IF 0.4 Q4 MATHEMATICS

Annales Mathematicae Silesianae Pub Date : 2020-05-08 DOI:10.2478/amsil-2020-0006

Reza Farhadian, R. Jakimczuk

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引用次数: 3

摘要

摘要设{rn}n∈𝕅是满足渐近公式rn ~ αβn的严格递增非负实数序列，其中α， β为实数，α > 0， β > 1。本文证明了该数列与数e之间的一些极限，并建立了该数列的计数函数的一些渐近公式和极限。所有的结果都应用于数学中一些著名的数列。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Notes on a General Sequence

Abstract Let {rn}n∈𝕅 be a strictly increasing sequence of nonnegative real numbers satisfying the asymptotic formula rn ~ αβn, where α, β are real numbers with α > 0 and β > 1. In this note we prove some limits that connect this sequence to the number e. We also establish some asymptotic formulae and limits for the counting function of this sequence. All of the results are applied to some well-known sequences in mathematics.

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来源期刊

Annales Mathematicae Silesianae Mathematics-Mathematics (all)

CiteScore

0.60

自引率

25.00%

发文量

审稿时长

27 weeks