Bernoulli polynomials

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31: Karl Dilcher

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24 Bernoulli and Euler Polynomials

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32: Bibliography I

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The real roots of Bernoulli polynomials. Ann. Univ. Turku. Ser. A I 37, pp. 1–20.

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External Links:

MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.12(i).

Encodings:

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33: 18.2 General Orthogonal Polynomials

… ►The Bernoulli polynomials $B_n\left(x\right)$ and Euler polynomials $E_n\left(x\right)$ are examples of Sheffer polynomials which are not OP’s, see the generating functions (24.2.3) and (24.2.8). For other examples of Sheffer polynomials, not in DLMF, see Roman (1984). …

34: Bibliography D

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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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ISSN 0021-9045, Document, MathReview (Guillermo López Lagomasino), ZentralBlatt

Referenced by:

§24.11.

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Irreducibility of certain generalized Bernoulli polynomials belonging to quadratic residue class characters. J. Number Theory 25 (1), pp. 72–80.

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ISSN 0022-314X, Document, MathReview (T. Metsänkylä)

Referenced by:

§24.12(iii).

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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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External Links:

ISSN 0065-9266, MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.12(i), §24.12(iii), §24.16(ii).

Encodings:

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On multiple zeros of Bernoulli polynomials. Acta Arith. 134 (2), pp. 149–155.

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ISSN 0065-1036, Document, MathReview (Arnold M. Adelberg), ZentralBlatt

Referenced by:

§24.12(iv).

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BibTeX

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35: Bibliography L

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The real zeros of the Bernoulli polynomials. J. Approx. Theory 58 (2), pp. 124–150.

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ISSN 0021-9045, Document, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§24.12(i), §24.9.

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On the maxima and minima of Bernoulli polynomials. Amer. Math. Monthly 47 (8), pp. 533–538.

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External Links:

FullText, MathReview (W. E. Milne), ZentralBlatt

Referenced by:

§24.12(i), §24.9.

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Hermite polynomials in asymptotic representations of generalized Bernoulli, Euler, Bessel, and Buchholz polynomials. J. Math. Anal. Appl. 239 (2), pp. 457–477.

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ISSN 0022-247X, Document, MathReview (A. G. Law), ZentralBlatt

Referenced by:

§18.34(iii), §24.11, §24.16(i), §24.16(i).

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Uniform approximations of Bernoulli and Euler polynomials in terms of hyperbolic functions. Stud. Appl. Math. 103 (3), pp. 241–258.

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External Links:

ISSN 0022-2526, Document, Link, MathReview, ZentralBlatt

Referenced by:

§24.11, §24.11.

Encodings:

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Large degree asymptotics of generalized Bernoulli and Euler polynomials. J. Math. Anal. Appl. 363 (1), pp. 197–208.

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ISSN 0022-247X, Document, Link, MathReview (Richard B. Paris), ZentralBlatt

Referenced by:

§24.16(i), §24.16(i).

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36: 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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External Links:

ISSN 0065-1036, Pdf, MathReview (L. Skula), ZentralBlatt

Referenced by:

§24.12(iii).

Encodings:

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Integrals of products of Bernoulli polynomials. J. Math. Anal. Appl. 381 (1), pp. 10–16.

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ISSN 0022-247X, Document, FullText, MathReview (Pablo Manuel Román), ZentralBlatt

Referenced by:

§24.13(i), §24.13(i).

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A primer on Bernoulli numbers and polynomials. Math. Mag. 81 (3), pp. 178–190.

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External Links:

ISSN 0025-570X, MathReview Entry, ZentralBlatt

Referenced by:

§24.5(ii), Ch.24.

Encodings:

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37: Bibliography H

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An Euler-Maclaurin-type formula involving conjugate Bernoulli polynomials and an application to $\zeta (2m+1)$ . Commun. Appl. Anal. 1 (1), pp. 15–32.

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ISSN 1083-2564, MathReview (Pavel Guerzhoy), ZentralBlatt

Referenced by:

§24.16(iii).

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Bernoulli numbers and polynomials via residues. J. Number Theory 76 (2), pp. 178–193.

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External Links:

ISSN 0022-314X, Document, MathReview (L. Skula), ZentralBlatt

Referenced by:

§24.14(ii).

Encodings:

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38: Bibliography B

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On the Euler and Bernoulli polynomials. J. Reine Angew. Math. 234, pp. 45–64.

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ISSN 0075-4102, MathReview (L. Carlitz), ZentralBlatt

Referenced by:

§24.12(iv).

Encodings:

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Bernoulli polynomials and asymptotic expansions of the quotient of gamma functions. J. Comput. Appl. Math. 235 (11), pp. 3315–3331.

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ISSN 0377-0427, Document, FullText, MathReview (Roberto S. Costas-Santos), ZentralBlatt

Referenced by:

§5.11(iii), §5.11(iii).

Encodings:

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Bernoulli numbers and polynomials of arbitrary complex indices. Appl. Math. Lett. 5 (6), pp. 83–88.

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External Links:

ISSN 0893-9659, MathReview, ZentralBlatt

Referenced by:

§24.16(iii).

Encodings:

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39: Bibliography K

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On the degree of an irreducible factor of the Bernoulli polynomials. Acta Arith. 50 (3), pp. 243–249.

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External Links:

ISSN 0065-1036, Pdf, MathReview (Wells Johnson), ZentralBlatt

Referenced by:

§24.12(iii).

Encodings:

BibTeX

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40: 3.11 Approximation Techniques

… ►For splines based on Bernoulli and Euler polynomials, see §24.17(ii). …