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Probabilistic proof...
Abstract
Ämnesord
Stäng
- 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
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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