﻿ 关于Glaisher-Kinkelin常数A的类似常数B的渐近展开 The Asymptotic Expansion Related to the Similar Constant B of Glaisher-Kinkelin Constant A

Vol.05 No.04(2016), Article ID:19031,5 pages
10.12677/AAM.2016.54075

The Asymptotic Expansion Related to the Similar Constant B of Glaisher-Kinkelin Constant A

Chaomin Tang*, Hongmei Liu, Yunxiao Shi, Guiqing Shi

School of Science, Dalian Nationalities University, Dalian Liaoning

Received: Nov. 2nd, 2016; accepted: Nov. 18th, 2016; published: Nov. 24th, 2016

ABSTRACT

In this paper, by the Bernoulli numbers and the exponential complete Bell polynomials, we establish one general asymptotic expansion related to the similar constant B of Glaisher-Kinkelin constant A and the function.

Keywords:Glaisher-Kinkelin Constant A, Similar Constant B, Asymptotic Expansion

1. 引言

Glaisher-Kinkelin常数被定义为：

，(1.1)

， (1.2)

.(1.3)

(1.4)

.(1.5)

. (1.6)

. (1.7)

. (1.8)

2. 定理及证明

2.1. 定理

， (2.1)

2.2. 证明

，由(1.6)以及的定义，我们可以将式(1.4)改写为：

.

.

.

.

3. 例子

.

The Asymptotic Expansion Related to the Similar Constant B of Glaisher-Kinkelin Constant A[J]. 应用数学进展, 2016, 05(04): 646-650. http://dx.doi.org/10.12677/AAM.2016.54075

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*通讯作者。