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    Boole Polynomial

    Definition

    Polynomials s_k(x;λ) which form a Sheffer sequence with g(t) | = | 1 + e^(λ t) f(t) | = | e^t - 1 and have generating function sum_(k = 0)^∞ (s_k(x;λ))/(k!) t^k = (1 + t)^x/(1 + (1 + t)^λ). The first few are s_0(x;λ) | = | 1/2 s_1(x;λ) | = | 1/4(2x - λ) t s_2(x;λ) | = | 1/4[2x(x - λ - 1) + λ].

    Related term

    Peters polynomial

    Associated person

    George Boole

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