Knar's Formula

Author

Eric W. Weisstein
October 5, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/KnarsFormula.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/KnarsFormula.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Formula

(2^(2 v)) (∏_m^∞)(1/(Sqrt[π])) (Gamma[(2^(-m)) v+(1/2)])==(Gamma[v+1])

V6

(2^(2v))Product[(π^(-1/2))Gamma[(1/2)+(2^(-m))v],{m,∞}]//Timing

V7

(2^(2v))Product[(π^(-1/2))Gamma[(1/2)+(2^(-m))v],{m,∞}]

Check

Subtract@@@Table[{Gamma[1+v],(2^(2v))Product[(π^(-1/2))Gamma[(1/2)+(2^(-m))v],{m,100}]}/.v->Random[Complex,2{-(I+1),I+1}],{100}]//N//Chop//Union