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

 * $\ds \sum_{n \mathop = 0}^\infty \frac {\paren {-1}^n} {\paren {2 n + 1}^s} = \frac 1 {\map \Gamma s} \int_1^\infty \frac {\ln^{s - 1} x} {x^2 + 1} \rd x$