User:GFauxPas/Sandbox

Welcome to my sandbox, you are free to play here as long as you don't track sand onto the main wiki. --GFauxPas 09:28, 7 November 2011 (CST)

User:GFauxPas/Sandbox/Zeta2/lnxln1-x/existence

User:GFauxPas/Sandbox/Zeta2/lnxln1-x/integrand

User:GFauxPas/Sandbox/Zeta2/lnxln1-x/evaluation

User:GFauxPas/Sandbox/Zeta2/FourierSeries/

User:GFauxPas/Sandbox/Zeta2/Informal Proof

Proof Technique
Let $x = \tan \dfrac \theta 2$

for $-\pi < \theta < \pi$.

From Shape of Tangent Function, this substitution is valid for all real $x$.

Let $2u = \theta$.

Then $x = \tan u$.

Observe:

Also,

Lastly,

Summarizing: