Dirichlet Beta Function at Odd Positive Integers/Examples

Examples of Values of Dirichlet Beta Function

Dirichlet Beta Function of $1$

$\map \beta 1 = \dfrac \pi 4 $

Dirichlet Beta Function of $3$

$\map \beta 3 = \dfrac {\pi^3} {32} $

Dirichlet Beta Function of $5$

$\map \beta 5 = \dfrac {5 \pi^5} {1536} $