proof that η(1)=ln2

Theorem 1.

η(1)=ln2, where η is the Dirichlet eta functionMathworldPlanetmath.

Proof. By definition,


Applying Abel’s Limit Theorem,

Title proof that η(1)=ln2
Canonical name ProofThateta1ln2
Date of creation 2013-03-22 17:57:20
Last modified on 2013-03-22 17:57:20
Owner rm50 (10146)
Last modified by rm50 (10146)
Numerical id 6
Author rm50 (10146)
Entry type Theorem
Classification msc 11M41