Lehmer's Constant

Author

Eric W. Weisstein
September 19, 2005

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/LehmersConstant.nb.

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

©2005 Wolfram Research, Inc. except for portions noted otherwise

Recurrence Equation

c[0]:=0
c[n_]:=c[n]=c[n-1]^2+c[n-1]+1

c/@Range[0,10]

V6

RSolve[{c[k]==c[k-1]^2+c[k-1]+1,c[0]==0},c[k],k]

V7

RSolve[{c[k]==c[k-1]^2+c[k-1]+1,c[0]==0},c[k],k]

Constant

ξ=Cot[FoldList[Plus,0,(ArcCot[c[#]](-1)^#&/@Range[0,20])]];//Timing

N[Last[ξ],200]

Block[{$MaxExtraPrecision=10^5},N[#,10]&/@(Subtract@@@Partition[ξ,2,1])]//Timing