论文标题
巴塞尔问题
The Basel Problem
论文作者
论文摘要
由于其与质子数的分布有关，Riemann Zeta函数ζ（S）是数学中最重要的功能之一。 ZETA函数由以下公式定义为任何复数数字s，实际分量大于1.Taking s = 2，我们看到ζ（2）等于所有正整数的倒数平方之和。这导致了巴塞尔在数学分析中的著名问题，其与数字理论的重要相关性，由莱昂哈德·欧拉（Leonhard Euler）于1734年解决。在本文中，我们讨论了数学家对基础问题的一些显着证明。大多数定理是非常众所周知的，而有些定理可以作为教科书中存在的问题证明。我们还使用残基的计算理论给出了一个新的证明。
Because of its relation to the distribution of prime numbers, the Riemann zeta function ζ (s) is one of the most important functions in mathematics. The zeta function is defined by the following formula for any complex number s with the real component greater than 1.Taking s=2, we see that ζ(2) is equal to the sum of the squares of reciprocals of all positive integers. This leads to the famous problem by Basel in mathematical analysis with important relevance to number theory, solved by Leonhard Euler in 1734. In this paper, we discuss some of the notable proofs given by mathematicians to the basal problem. Most of the theorems are very well known whereas some can be found as proofs of problems present in textbooks.We also give one new proof using the theory of calculus of residues.
