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    Actuarial Polynomial

    Definition

    The polynomials a_n^(β)(x) given by the Sheffer sequence with g(t) | = | (1 - t)^(-β) f(t) | = | ln(1 - t), giving generating function sum_(k = 0)^∞ a_n^(β)/(k!) t^k = e^(x(1 - e^t) + β t). The Sheffer identity is a_n^(β)(x + y) = sum_(k = 0)^n(n k) a_k^(β)(y) ϕ_(n - k)(-x), where ϕ_n(x) is a Bell polynomial.

    Related term

    Sheffer sequence

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