Equation for Dirichlet beta and Riemann zeta functions

Question

given the series $$ B (s)=\sum_{n=1}^{\infty}\frac{(-1)^n}{(2n-1)^s} $$

is there a realtion (functional relation) with other series like Riemann zeta function

or $$ \lambda (s)= \sum_{n=1}^{\infty}\frac{1}{(2n-1)^s}$$