Wallis Formula

​
terms
4
∏
n=1
2
(2n)
(-1+2n)(1+2n)
= 1.48608
The slowly convergent Wallis formula for
π
2
=
∞
∏
n=1
2
(2n)
(-1+2n)(1+2n)
=1.57079...
follows from the infinite product representation for
sin(x)=x
∞
∏
n=1
1-
2
x
2
n
2
π
, when
x=
π
2
.
At each step, the outermost green segment represents the cumulative value of the product and the yellow segment represents the error relative to
π
2
.

External Links

Wallis Formula (Wolfram MathWorld)

Permanent Citation

Michael Schreiber
​
​"Wallis Formula"​
​http://demonstrations.wolfram.com/WallisFormula/​
​Wolfram Demonstrations Project​
​Published: September 28, 2007