Sum of Reciprocals of Powers of Odd Integers Alternating in Sign/Corollary

Corollary to Sum of Reciprocals of Powers of Odd Integers Alternating in Sign

 * $\displaystyle \sum_{n \mathop = 0}^\infty \frac {\left({-1}\right)^n} {\left({2 n + 1}\right)^s} = \frac 1 {\Gamma\left({s}\right)} \int_1^\infty \frac {\ln^{s - 1} x} {x^2 + 1} \rd x$