Linkage to the Riemann Zeta Function
The Riemann zeta function is one of the most significant functions in mathematics because of its relationship to distribution of prime numbers. And the solution for this Basel problem provided a conjunction point for connecting Riemann zeta function to this problem. It had major implications at that time. Eventually, mathematicians also had to admit its efficiency and they admitted it. This was not first time but, when Euler didn’t have a certain justification for a problem. Just like every other proof, he even proved existing solution to this problem!
Read More: Riemann Sums
Basel Problem
The Basel problem is an issue of Pietro Mengoli’s theory of numbers in 1644 and Leonhard Euler’s resolution in 1734. Since Euler’s solution stayed open for 90 years, at the age of 28 he was immediately renowned for discovering solutions to this problem.
This problem asks for the sum of the inverse of the square number. Initially, it may sound somewhat confusing, but after reading this article you will be clear about concept and approach to this problem.
Table of Content
- What is the Basel Problem?
- How to Find Inverse using Basel Problem?
- Proof
- Linkage to the Riemann Zeta Function