Norton's Constant

Author

Eric W. Weisstein
August 5, 2008

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

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

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

Value

(PorterConstant=-((Pi^2+12 Log[2] (2+Log[2]-48 Log[Glaisher]+4 Log[Pi]))/(2 Pi^2)))//N

<<Utilities`Simplify`

FullSimplify[((12Log[2])/(π^2))(-(1/2)+(6/(π^2))Zeta'[2])+PorterConstant-(1/2)]//LogExpand

FullSimplify[%]

N[-(1/(π^2))((π^2)-6 Log[2] (-3+2 EulerGamma+Log[2]+24 Log[Glaisher]-2 Log[π])),20]