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Consider the sequence $\{B_r(x)\}_{r=0}^{\infty}$ of polynomials defined using the recursion: $ \begin{aligned} B_0(x) &= 1 \\ B_r^\prime(x) &= r B_{r-1}(x) \quad \forall r\geq 1 \\ \int_0^1 B_r(x) dx &= 0 \quad \forall r\geq 1 \end{aligned} $ The first few Bernoulli … Continue reading →