Nielsen-Ramanujan Constants

Author

Eric W. Weisstein
August 13, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/Nielsen-RamanujanConstants.nb.

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

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

Definition

i[k_]:=Integrate[Log[x]^k/(x-1),{x,1,2}]

i[k]

Table

FullSimplify[Table[{k,i[k]},{k,5}]]//TableForm

Analytic

a[p_]:=p! Zeta[p+1]-((p ((Log[2])^(p+1)))/(p+1))-p! Sum[((PolyLog[p+1-k,1/2](Log[2])^k)/(k!)),{k,0,p-1}]

Simplify[Table[a[p]-i[p],{p,5}]]

V7

FullSimplify[a[p]]

Table[a[p],{p,5}]//FullSimplify