Masser-Gramain Constant

Author

Eric W. Weisstein
February 8, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/Masser-GramainConstant.nb.

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

©2006 Wolfram Research, Inc. except for portions noted otherwise

log(((Subscript[M, r])/r))

N[Log[2],20]

α

N[α=Pi/2/E,20]

c

Numeric

N[c=(1/4)π(2EulerGamma+2Log[2]+3Log[Pi]-4Log[Gamma[(1/4)]]),20]

v5.2

c=EulerGamma DirichletBeta[1]+Limit[Derivative[1][DirichletBeta][x],x->1]

v6

<<Utilities`Simplify`

c=EulerGamma DirichletBeta[1]+Limit[Derivative[1][DirichletBeta][x],x->1]

%38//N

Factor[Expand[LogExpand[GammaSimplify[FunctionExpand[c]]]]]

N[%]

((4 c)/π)+1

N[δ=4c/π+1,20]