Bernoulli
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31—40 of 66 matching pages
31: 17.3 -Elementary and -Special Functions
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§17.3(iii) Bernoulli Polynomials; Euler and Stirling Numbers
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17.3.7
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βΊThe are, in fact, rational functions of , and not necessarily polynomials.
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32: 5.15 Polygamma Functions
33: 2.10 Sums and Sequences
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βΊAs in §24.2, let and denote the th Bernoulli number and polynomial, respectively, and the th Bernoulli periodic function .
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2.10.1
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2.10.4
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2.10.5
βΊFrom §24.12(i), (24.2.2), and (24.4.27), is of constant sign .
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34: 25.6 Integer Arguments
35: 25.16 Mathematical Applications
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25.16.6
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25.16.7
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25.16.10
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has a simple pole with residue () at each odd negative integer , .
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36: 5.17 Barnes’ -Function (Double Gamma Function)
37: Bibliography D
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Sur les zéros réels des polynômes de Bernoulli.
Ann. Inst. Fourier (Grenoble) 41 (2), pp. 267–309 (French).
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Asymptotic behaviour of Bernoulli, Euler, and generalized Bernoulli polynomials.
J. Approx. Theory 49 (4), pp. 321–330.
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Zeros of Bernoulli, generalized Bernoulli and Euler polynomials.
Mem. Amer. Math. Soc. 73 (386), pp. iv+94.
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Sums of products of Bernoulli numbers.
J. Number Theory 60 (1), pp. 23–41.
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Bernoulli Numbers and Confluent Hypergeometric Functions.
In Number Theory for the Millennium, I (Urbana, IL, 2000),
pp. 343–363.
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38: 19.30 Lengths of Plane Curves
39: Bibliography T
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New congruences for the Bernoulli numbers.
Math. Comp. 48 (177), pp. 341–350.
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Bernoulli polynomials old and new: Generalizations and asymptotics.
CWI Quarterly 8 (1), pp. 47–66.
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Explicit formulas for the Bernoulli and Euler polynomials and numbers.
Abh. Math. Sem. Univ. Hamburg 61, pp. 175–180.
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On the theory of the Bernoulli polynomials and numbers.
J. Math. Anal. Appl. 104 (2), pp. 309–350.
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40: Bibliography H
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An Euler-Maclaurin-type formula involving conjugate Bernoulli polynomials and an application to
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Commun. Appl. Anal. 1 (1), pp. 15–32.
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An explicit formula for Bernoulli numbers.
Rep. Fac. Sci. Technol. Meijo Univ. 29, pp. 1–6.
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On congruences involving Bernoulli numbers and irregular primes. II.
Rep. Fac. Sci. Technol. Meijo Univ. 31, pp. 1–8.
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Explicit formulas for degenerate Bernoulli numbers.
Discrete Math. 162 (1-3), pp. 175–185.
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Bernoulli numbers and polynomials via residues.
J. Number Theory 76 (2), pp. 178–193.
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