A formula which expresses the number as an infinite product:
There exist other variants of this formula, e.g.:
Formula (1) was first employed by J. Wallis  in his calculation of the area of a disc; it is one of the earliest examples of an infinite product.
|||J. Wallis, "Arithmetica infinitorum" , Oxford (1656)|
Formula (1) is a direct consequence of Euler's product formula
It can also be obtained by expressing and in terms of , and by showing that
Formula (2) can be derived from (1) by multiplying the numerator and the denominator of by .
|[a1]||T.M. Apostol, "Calculus" , 2 , Blaisdell (1964)|
|[a2]||C.H. Edwards jr., "The historical development of the calculus" , Springer (1979)|
|[a3]||P. Lax, S. Burstein, A. Lax, "Calculus with applications and computing" , 1 , Springer (1976)|
|[a4]||D.J. Struik (ed.) , A source book in mathematics: 1200–1800 , Harvard Univ. Press (1986)|
Wallis formula. T.Yu. Popova (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Wallis_formula&oldid=13195