Golomb-Dickman Constant

Author

Eric W. Weisstein
July 25, 2013

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/Golomb-DickmanConstant.nb.

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

©2013 Wolfram Research, Inc. except for portions noted otherwise

α

Mean

V6

Sum[1/i,{i,n}]

Simplify[Series[FunctionExpand[%],{n,∞,5}],n>0]

V7

Sum[1/i,{i,n}]

Simplify[Series[HarmonicNumber[n],{n,∞,1}],n>0]

Variance

V6

Sum[(i-1)/i^2,{i,n}]

FullSimplify[Series[FunctionExpand[%],{n,∞,2}],n>0]

Normal[%]

V7

Sum[(i-1)/i^2,{i,n}]

Simplify[Series[HarmonicNumber[n]-HarmonicNumber[n,2],{n,∞,2}],Assumptions->n>0]

λ exact via integral

V5

Table[LogIntegral[x]-NIntegrate[1/Log[y],{y,0,x},WorkingPrecision->20],{x,0,.99,.1}]//Chop

Integrate[1/Log[y],{y,0,x},Assumptions->0<x<1]

Integrate[1/Log[y],{y,0,x},GenerateConditions->False]

Integrate[Exp[LogIntegral[x]],{x,0,1}]

λ=NIntegrate[Exp[LogIntegral[x]],{x,0,1},WorkingPrecision->110,MaxRecursion->20]

V5.2

Integrate[Exp[LogIntegral[x]],{x,0,1}]

V6

Integrate[Exp[LogIntegral[x]],{x,0,1}]

V8

Integrate[Exp[LogIntegral[x]],{x,0,1}]

V9

Integrate[Exp[LogIntegral[x]],{x,0,1}]

V10

Integrate[Exp[LogIntegral[x]],{x,0,1}]