Bernoulli and Euler polynomials
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31—40 of 46 matching pages
31: 25.1 Special Notation
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nonnegative integers. | |
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Euler’s constant (§5.2(ii)). | |
digamma function except in §25.16. See §5.2(i). | |
Bernoulli number and polynomial (§24.2(i)). | |
periodic Bernoulli function . | |
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32: Errata
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Equation (5.17.5)
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5.17.5
Originally the term was incorrectly stated as .
Reported 2013-08-01 by Gergő Nemes and subsequently by Nick Jones on December 11, 2013.
33: Bibliography B
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On the Euler and Bernoulli polynomials.
J. Reine Angew. Math. 234, pp. 45–64.
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34: Bibliography C
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Some congruences for the Bernoulli numbers.
Amer. J. Math. 75 (1), pp. 163–172.
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-Bernoulli and Eulerian numbers.
Trans. Amer. Math. Soc. 76 (2), pp. 332–350.
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A note on Euler numbers and polynomials.
Nagoya Math. J. 7, pp. 35–43.
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Expansions of -Bernoulli numbers.
Duke Math. J. 25 (2), pp. 355–364.
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Accélération de calcul de nombres de Bernoulli.
J. Number Theory 28 (3), pp. 347–362 (French).
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35: 25.11 Hurwitz Zeta Function
36: 25.16 Mathematical Applications
37: 2.10 Sums and Sequences
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§2.10(i) Euler–Maclaurin Formula
►As in §24.2, let and denote the th Bernoulli number and polynomial, respectively, and the th Bernoulli periodic function . … ►This is the Euler–Maclaurin formula. … ►From §24.12(i), (24.2.2), and (24.4.27), is of constant sign . … ►Example
…38: 25.2 Definition and Expansions
39: 3.5 Quadrature
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►For the Bernoulli numbers see §24.2(i).
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Gauss–Legendre Formula
… ►In the case of Chebyshev weight functions on , with , the nodes , weights , and error constant , are as follows: … ►The are the monic Hermite polynomials (§18.3). … ► …40: Bibliography
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Integrals of products of Bernoulli polynomials.
J. Math. Anal. Appl. 381 (1), pp. 10–16.
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Some determinants of Bernoulli, Euler and related numbers.
Portugal. Math. 18, pp. 91–99.
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Bernoulli’s power-sum formulas revisited.
Math. Gaz. 90 (518), pp. 276–279.
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A primer on Bernoulli numbers and polynomials.
Math. Mag. 81 (3), pp. 178–190.
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