Bernoulli polynomials
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11: 24.9 Inequalities
12: 24.12 Zeros
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§24.12(i) Bernoulli Polynomials: Real Zeros
►In the interval the only zeros of , , are , and the only zeros of , , are . ►For the interval denote the zeros of by , , with … ►Let be the total number of real zeros of . … ► , , has no multiple zeros. …13: 5.11 Asymptotic Expansions
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5.11.8
►where is fixed, and is the Bernoulli polynomial defined in §24.2(i).
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►In terms of generalized Bernoulli polynomials
(§24.16(i)), we have for ,
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5.11.17
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5.11.18
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14: 24.14 Sums
§24.14 Sums
►§24.14(i) Quadratic Recurrence Relations
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24.14.1
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24.14.5
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►For other sums involving Bernoulli and Euler numbers and polynomials see Hansen (1975, pp. 331–347) and Prudnikov et al. (1990, pp. 383–386).
15: 25.11 Hurwitz Zeta Function
16: 24.8 Series Expansions
17: 24.7 Integral Representations
18: 25.2 Definition and Expansions
19: 17.3 -Elementary and -Special Functions
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§17.3(iii) Bernoulli Polynomials; Euler and Stirling Numbers
►-Bernoulli Polynomials
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17.3.7
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►The are, in fact, rational functions of , and not necessarily polynomials.
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