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    Mahler Polynomial

    Definition

    Polynomials s_n(x) which form the Sheffer sequence for f^(-1)(t) = 1 + t - e^t, where f^(-1)(t) is the inverse function of f(t), and have generating function sum_(k = 0)^∞ (s_k(x))/(k!) t^k = e^(x(1 + t - e^t)). The first few are s_0(x) | = | 1 s_1(x) | = | 0 s_2(x) | = | -x s_3(x) | = | -x s_4(x) | = | 3x^2 - x s_5(x) | = | 10x^2 - x.

    Associated person

    Kurt Mahler

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