Basel problem

English

Etymology

Named after Basel, the home town of Euler and of the Bernoulli family who unsuccessfully attacked the problem.

Proper noun

Basel problem

1. (mathematics) The question as to the value of $\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}$, the sum of the reciprocals of the squares of the positive integers.
   • 1999, William Dunham, Euler: The Master of Us All, Mathematical Association of America, →ISBN, page 55:

     As noted, some of Euler's contemporaries, while accepting his answer to the Basel Problem, wondered about the validity of the argument that got him there.

   • 2005, Rajendra Bhatia, Fourier Series, Mathematical Association of America, →ISBN, section 3.10, page 75:

     Solving the Basel problem was one of the early triumphs of L. Euler (1707–1783)... .

   • 2007, Charles Edward Sandifer, The Early Mathematics of Leonhard Euler, Mathematical Association of America, →ISBN, page 165:

     And so ends one of Euler's most famous papers. We see that Euler actually solves the Basel problem three times and that he does much more.