Basel problem
Solución del problema de Basilea: suma de 1/n^2 = pi^2/6
- Date
- 1735 · confidence high
- Place
- St Petersburg, Russia
- Credited to
- Leonhard Euler
- People
- 👤 Leonhard Euler1707–1783
- Field
- Knowledge & symbols
What was discovered
The exact calculation of the sum of the reciprocals of the squares, which had resisted the Bernoullis, by factorising the sine as an infinite product. It revealed an unexpected connection between the integers and pi.
The rigorous justification of the infinite product came with Weierstrass; Euler later gave several alternative proofs.
What it led to
- the Riemann zeta function
- Euler's product over the primes
- analytic number theory
Built on
- Leibniz and Bernoulli series