relation%20to%20Bernoulli%20numbers

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11: Bibliography F

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Sur certaines sommes des intégral-cosinus. Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).

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External Links:

MathReview (L. Carlitz), ZentralBlatt

Referenced by:

§6.15.

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A Table of the Complete Elliptic Integral of the First Kind for Complex Values of the Modulus. Part I. Technical report Technical Report ARL 69-0172, Aerospace Research Laboratories, Office of Aerospace Research, Wright-Patterson Air Force Base, Ohio.

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Notes:

Table erratum: Math. Comp. v. 36 (1981), no. 153, p. 318. Part II of this report, with the same date but numbered ARL 69-0173, again puts $k=R\exp (i\theta )$ but with $R$ as parameter and $\theta$ as variable instead of the other way around. Part III, dated May 1970 and numbered ARL 70-0081, contains tables of auxiliary functions to help interpolation.

External Links:

MathReview, ZentralBlatt

Referenced by:

§19.36(ii), §19.37(ii).

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Numerical calculation of singular integrals related to Hankel transform. Comput. Math. Appl. 21 (2-3), pp. 87–94.

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Notes:

Fortran, minimum precision 6D.

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ISSN 0898-1221, Document, MathReview, ZentralBlatt

Referenced by:

§10.77(ix).

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Faster computation of Bernoulli numbers. J. Algorithms 13 (3), pp. 431–445.

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ISSN 0196-6774, MathReview (P. K. Subramanian), ZentralBlatt

Referenced by:

§24.19(i).

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Introduction to the Random Matrix Theory: Gaussian Unitary Ensemble and Beyond. In Recent Perspectives in Random Matrix Theory and Number Theory, London Math. Soc. Lecture Note Ser., Vol. 322, pp. 31–78.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§18.38(ii).

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12: Bibliography K

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Poly-Bernoulli numbers. J. Théor. Nombres Bordeaux 9 (1), pp. 221–228.

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ISSN 1246-7405, PostScript, MathReview (L. Skula), ZentralBlatt

Referenced by:

§24.16(iii).

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The congruences of Clausen-von Staudt and Kummer for Bernoulli-Hurwitz numbers. Math. Ann. 216 (1), pp. 1–4.

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ISSN 0025-5831, Document, MathReview (M. Basmakov), ZentralBlatt

Referenced by:

§24.16(iii).

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On formulas involving both the Bernoulli and Fibonacci numbers. Scripta Math. 23, pp. 27–35.

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External Links:

MathReview (L. Carlitz), ZentralBlatt

Referenced by:

§24.15(iv).

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Remark on $p$-adic $q$-Bernoulli numbers. Adv. Stud. Contemp. Math. (Pusan) 1, pp. 127–136.

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Notes:

Algebraic number theory (Hapcheon/Saga, 1996)

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ISSN 1229-3067, MathReview (L. Skula), ZentralBlatt

Referenced by:

§24.16(iii).

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Computation of tangent, Euler, and Bernoulli numbers. Math. Comp. 21 (100), pp. 663–688.

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External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§24.15(ii), §24.19(i).

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13: Bibliography D

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Bernoulli Numbers. Bibliography (1713–1990). Queen’s Papers in Pure and Applied Mathematics, Vol. 87, Queen’s University, Kingston, ON.

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Notes:

A frequently updated version, with links to reviews, exists online

External Links:

Online version, MathReview, ZentralBlatt

Referenced by:

Ch.24.

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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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Sums of products of Bernoulli numbers. J. Number Theory 60 (1), pp. 23–41.

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ISSN 0022-314X, Document, MathReview (Wen Peng Zhang), ZentralBlatt

Referenced by:

§24.14(ii).

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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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External Links:

ISBN 1-56881-126-8, MathReview (Arnold M. Adelberg), ZentralBlatt

Referenced by:

§24.16(iii).

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