Resumen de Probabilistic proofs of euler identities

Lars Holst

• Formulae for £(2n) and L?4 (2n + 1) involving Euler and tangent numbers are derived using the hyperbolic secant probability distribution and its moment generating function. In particular, the Basel problem, where ?(2) = p²/6, is considered. Euler's infinite product for the sine is also proved using the distribution of sums of independent hyperbolic secant random variables and a local limit theorem