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Faculty Publication: Research Associate in Mathematics Bill Dunham

April 22, 2021

Author: Bill Dunham

Source: The American Mathematical Monthly, vol. 128, no. 4, 2021.

Publication type: Article

Abstract: In 1734, Leonhard Euler summed the infinite series of reciprocals of the squares, thereby solving a challenge known as the 鈥淏asel problem.鈥 He later extended his method to find closed-form sums for the reciprocals of 4th, 6th, 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.

Department of Mathematics

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