Flajolet-Odlyzko Constant

Author

Eric W. Weisstein
August 5, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/Flajolet-OdlyzkoConstant.nb.

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

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

Value

G(a,n)==(1/a)(∫_0^∞)(1-(E^(a Ei(-t))) (∑_(k=0)^(n-1))(((((-a))^k) ((Ei(-t))^k))/(k!)))\[DifferentialD]t

(∑_(k=0)^(n-1))(((((-a))^k) ((ExpIntegralEi[-t])^k))/(k!))

(1-(E^(a ExpIntegralEi[-t])) (((E^(-a ExpIntegralEi[-t])) Gamma[n,-a ExpIntegralEi[-t]])/(Gamma[n])))

G[a_,n_]:=(1/a)(∫_0^∞)(1-(E^(a ExpIntegralEi[-t])) (∑_(k=0)^(n-1))(((((-a))^k) ((ExpIntegralEi[-t])^k))/(k!)))\[DifferentialD]t

G[a_,n_]:=(1/a)Integrate[1-((Gamma[n,-a ExpIntegralEi[-t]])/(Gamma[n])),{t,0,∞}]

G[1/2,1]

N[%]

N[G[1/2,1],100]