Iseki's Formula

Author

Eric W. Weisstein
September 20, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/NumberTheory/IsekisFormula.nb.

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

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

Sums

Sum[((Exp[-2π m x])/m),{m,∞}]

Sum[((Exp[-2π m x])/m),{m,∞}]

FullSimplify[%]

-π z Sum[Binomial[2,n](((I z))^(-n))BernoulliB[2-n,α]BernoulliB[n,β],{n,0,2}]