6. Wallis and Pippenger Infinite Products

The Wallis product is a formula found in 1655 by John Wallis, which calculates the simple infinite product:

 

Nick Pippenger obtained an infinite product for  e:

http://en.wikipedia.org/wiki/Wallis_product

http://en.wikipedia.org/wiki/Infinite_product#Product_representations_of_functions

http://mathworld.wolfram.com/WallisFormula.html

http://mathworld.wolfram.com/PippengerProduct.html

http://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80

http://en.wikipedia.org/wiki/Vi%C3%A8te%27s_formula

 

From the Wallis formula you can also get:

In Wolfram MathWorld site:

http://mathworld.wolfram.com/InfiniteProduct.html

 
you can find an extensive list of infinite products. In particular, the formula obtained above is a simple case (21) of a more general set (D.W.Cantrell, 2006)