Formulae for ζ(2n) and Lχ4 (2n + 1) involving Euler and tangent numbers are derived using the hyperbolic secant probability distribution and its moment generating function. In particular, the Basel ...

Let f be an analytic and univalent function on a simply connected domain D, and let λD be the hyperbolic metric on D. We prove the sharp inequality $\left| {\frac{{{f^n}\left( w \right)}}{{f\left( w ...