Probabilistic proofs of euler identities

• Formulae for zeta(2n) and L-chi 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 zeta(2) = pi(2)/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.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Basel problem

hyperbolic secant distribution

Euler number

tangent number

Euler's sine product

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