A Note on the Multiplication Formulas for the Bernoulli and Euler Polynomials
نویسنده
چکیده
where J5m(x), Em(x) denote the polynomials of Bernoulli and Euler in the usual notation. It is perhaps not so familiar that (1.1) and (1.2) characterize the polynomials. More precisely, as Nielsen has pointed out [3, p. 54], if a normalized polynomial satisfies (1.1) for a single value k>l, then it is identical with Bm(x); similarly if a normalized polynomial satisfies (1.2) for a single odd k>l, then it is identical with Em(x). For some generalizations see [l]. The situation for (1.3) is clearly different. For consider the equation
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