Bernoulli and Euler numbers
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11—20 of 51 matching pages
11: 17.3 -Elementary and -Special Functions
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§17.3(iii) Bernoulli Polynomials; Euler and Stirling Numbers
…12: 24.19 Methods of Computation
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§24.19(i) Bernoulli and Euler Numbers and Polynomials
►Equations (24.5.3) and (24.5.4) enable and to be computed by recurrence. … ►For algorithms for computing , , , and see Spanier and Oldham (1987, pp. 37, 41, 171, and 179–180). …13: 24.4 Basic Properties
14: 24.13 Integrals
15: 4.19 Maclaurin Series and Laurent Series
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►In (4.19.3)–(4.19.9), are the Bernoulli numbers and are the Euler numbers (§§24.2(i)–24.2(ii)).
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16: 24.7 Integral Representations
17: 24.15 Related Sequences of Numbers
§24.15 Related Sequences of Numbers
►§24.15(i) Genocchi Numbers
… ►§24.15(ii) Tangent Numbers
… ►§24.15(iii) Stirling Numbers
… ►§24.15(iv) Fibonacci and Lucas Numbers
…18: 24.8 Series Expansions
19: 24.17 Mathematical Applications
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§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)). …20: 24.16 Generalizations
§24.16 Generalizations
… ►When they reduce to the Bernoulli and Euler numbers of order : … ►
24.16.13
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