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On reading Bernoulli’s Ars conjectandi 1713

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James Bernoulli’s posthumous book is famous among statisticians for the binomial distribution in Part I, the Bernoulli numbers in Part II and the limit theorem in Part IV, but it contains much else of interest besides. It is full of Pascal triangles, and Bernoulli’s treatment of the polynomials for the sums of the powers of the integers leads to the discovery that the Bernoulli numbers had already been published by Johann Faulhaber in 1631. We can now see how Bernoulli derived the polynomials; the simple algorithm reveals an error in his table of the coefficients. An alternative and elegant procedure involves the inversion of Pascal matrices of binomial coefficients.

This talk is part of the Cambridge Statistics Discussion Group (CSDG) series.

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