$$\sum\limits_{k = 0}^{ + \infty } {\frac{1}{{\cosh \left( {\pi k} \right)}}} = \frac{1}{2} + \frac{1}{{{\rm B}\left( {\frac{3}{4},\frac{3}{4}} \right)}}.$$ $$\sum\limits_{k = 0}^{ + \infty } {\frac{{{{\left( { - 1} \right)}^k}}}{{\cosh \left( {\pi k} \right)}}} = \frac{1}{2} + \frac{1}{{{\rm B}\left( {\frac{1}{2},\frac{3}{4}} \right)}}.$$