One may define the Bernoulli numbers B, as the coefficients of the following power series: Bnzn = e² - 1 n! n=0 a) Let y

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One May Define The Bernoulli Numbers B As The Coefficients Of The Following Power Series Bnzn E 1 N N 0 A Let Y 1 (49.29 KiB) Viewed 24 times

One may define the Bernoulli numbers B, as the coefficients of the following power series: Bnzn = e² - 1 n! n=0 a) Let y be the positively-oriented circle |z| = 1. Show that: n! dz Bn = if 2πi zn (ez - 1)' b) Find and classify all isolated singularities for the complex function 1 fn(z) = n = 0, 1, 2... zn (ez - 1)' c) Compute Res (fn (2), z = 0) for n = 0, 1, and use that to show Bo = 1, B₁ = 2