Bernoulli
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11: 24.21 Software
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§24.21(ii) , , , and
…12: 24.10 Arithmetic Properties
§24.10 Arithmetic Properties
►§24.10(i) Von Staudt–Clausen Theorem
… ►§24.10(ii) Kummer Congruences
… ►§24.10(iii) Voronoi’s Congruence
… ►§24.10(iv) Factors
…13: 25.1 Special Notation
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nonnegative integers. | |
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Bernoulli number and polynomial (§24.2(i)). | |
periodic Bernoulli function . | |
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14: 24.17 Mathematical Applications
§24.17 Mathematical Applications
… ►Bernoulli Monosplines
… ►§24.17(iii) Number Theory
►Bernoulli and Euler numbers and polynomials occur in: number theory via (24.4.7), (24.4.8), and other identities involving sums of powers; the Riemann zeta function and -series (§25.15, Apostol (1976), and Ireland and Rosen (1990)); arithmetic of cyclotomic fields and the classical theory of Fermat’s last theorem (Ribenboim (1979) and Washington (1997)); -adic analysis (Koblitz (1984, Chapter 2)).15: 24.9 Inequalities
16: 24.6 Explicit Formulas
17: 24.7 Integral Representations
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§24.7(i) Bernoulli and Euler Numbers
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24.7.1
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24.7.3
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24.7.4
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§24.7(ii) Bernoulli and Euler Polynomials
…18: 24.15 Related Sequences of Numbers
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§24.15(i) Genocchi Numbers
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24.15.2
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§24.15(ii) Tangent Numbers
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24.15.4
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§24.15(iii) Stirling Numbers
…19: 24 Bernoulli and Euler Polynomials
Chapter 24 Bernoulli and Euler Polynomials
…20: Karl Dilcher
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►Over the years he authored or coauthored numerous papers on Bernoulli numbers and related topics, and he maintains a large on-line bibliography on the subject.
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