# Wallis product

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In mathematics, the Wallis product for π, published in 1656 by John Wallis, states that

## Proof using integration

(This is a form of Wallis' integrals.)

This result will be used below:

Repeating the process,

Repeating the process,

By the squeeze theorem,

## Proof using Euler's infinite product for the sine function

While the proof above is typically featured in modern calculus textbooks, the Wallis product is, in retrospect, an easy corollary of the later Euler infinite product for the sine function.

## Relation to Stirling's approximation

## Derivative of the Riemann zeta function at zero

The Riemann zeta function and the Dirichlet eta function can be defined:

Applying an Euler transform to the latter series, the following is obtained:

## See also

Credits to the contents of this page go to the authors of the corresponding Wikipedia page: en.wikipedia.org/wiki/Wallis product.