 Dirichlet beta function

The Dirichlet beta function is $\beta (s)={\sum }_{n\ge 0}(-1{)}^n(2n+1{)}^{-s}$ and is the Dirichlet L-function for the nontrivial character modulo four.

The Dirichlet beta function, denoted as \( \beta(s) \), is a special function that generalizes the concept of the Riemann zeta function.