The Pippenger product is an unexpected Wallis-like formula for 
given by
 |
(1)
|
(OEIS A084148 and A084149; Pippenger 1980). Here, the 
th term for 
is given by
 |  | ![([(2^(n-1)-1)!!]^2[(2^n)!!]^2)/(2[(2^(n-1))!!]^2[(2^n-1)!!]^2)](/images/equations/PippengerProduct/Inline6.svg) |
(2)
|
 |  | ![(2^(2^n-1)[Gamma(1/2+2^(n-2))]^4)/(pi[Gamma(1/2+2^(n-1))]^2),](/images/equations/PippengerProduct/Inline9.svg) |
(3)
|
where 
is a double factorial and 
is the gamma function.
Pippenger Product
See also
e, Wallis FormulaExplore with Wolfram|Alpha
References
Pippenger, N. "An Infinite Product for
." Amer. Math. Monthly 87, 391, 1980.Sloane,
N. J. A. Sequences A084148 and A084149 in "The On-Line Encyclopedia of Integer
Sequences."Referenced on Wolfram|Alpha
Pippenger ProductCite this as:
Weisstein, Eric W. "Pippenger Product." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PippengerProduct.html