Gompertz Constant

Author

Eric W. Weisstein
September 7, 2008

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

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

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

Value

Integrate[((Exp[-u])/(1+u)),{u,0,∞}]

FullSimplify[%]

N[%,20]

Continued Fraction

FromGeneralContinuedFraction[{a0_,l_List?MatrixQ}]:=a0+Fold[#2[[1]]/(#1+#2[[2]])&,0,Reverse[l]]

Block[{$MaxExtraPrecision=500},
N[Subtract@@{-E ExpIntegralEi[-1],FromGeneralContinuedFraction[{0,Join[{{1,2}},Table[{-i^2,2i+2},{i,10000}]]}]},20]
]

(1/(2+ContinuedFractionK[-(n^2),2(n+1),{n,∞}]))

(1/(2+ContinuedFractionK[-(n^2),2(n+1),{n,20}]))//N

N[-E ExpIntegralEi[-1]]