Euler and the Cubic Basel Problem. Issue 4 (12th March 2021) - Dunham, William
Abstract: In 1734, Leonhard Euler summed the infinite series of reciprocals of the squares, thereby solving a challenge known as the "Basel problem." He later extended his method to find closed-form sums for the reciprocals of 4 th, 6 th, and other even powers. But those techniques did not yield a value for the sum of the reciprocals of the cubes . Here, we show how Euler tried to evaluate this series by transforming it into the sum of a strange constant and an even stranger integral.