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11: Roderick S. C. Wong

… ►Wong was elected a Fellow of the Royal Society of Canada in 1993, a Foreign Member of the Academy of Science of Turin, Italy, in 2001, a Chevalier dans l’Ordre National de la Légion d’Honneur in 2004, and a Member of the European Academy of Sciences in 2007. He was recipient of the Killam Research Fellowship from the Canada Council in 1982–1984, and of the Rh Award for Outstanding Contributions to Scholarship and Research from the University of Manitoba in 1984. …

12: 26.21 Tables

§26.21 Tables

►Abramowitz and Stegun (1964, Chapter 24) tabulates binomial coefficients $\left(\genfrac{}{}{0.0pt}{}{m}{n}\right)$ for $m$ up to 50 and $n$ up to 25; extends Table 26.4.1 to $n=10$; tabulates Stirling numbers of the first and second kinds, $s(n,k)$ and $S(n,k)$, for $n$ up to 25 and $k$ up to $n$; tabulates partitions $p\left(n\right)$ and partitions into distinct parts $p(𝒟,n)$ for $n$ up to 500. ►Andrews (1976) contains tables of the number of unrestricted partitions, partitions into odd parts, partitions into parts $\cancel{\equiv }\pm 2(mod5)$, partitions into parts $\cancel{\equiv }\pm 1(mod5)$, and unrestricted plane partitions up to 100. It also contains a table of Gaussian polynomials up to ${\left[\genfrac{}{}{0.0pt}{}{12}{6}\right]}_q$. ►Goldberg et al. (1976) contains tables of binomial coefficients to $n=100$ and Stirling numbers to $n=40$.

13: Bibliography S

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Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity. 4th edition, Springer-Verlag, Berlin.

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Notes:

Volume 7 in Springer Series in Information Sciences.

External Links:

ZentralBlatt

Referenced by:

§27.16, §27.17.

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The zeros and maxima of the Airy function and its first derivative to 25 significant figures. Report AFCRC-TR-59-135, ASTIA Document No. AD214568 Air Research and Development Command, U.S. Air Force, Bedford, MA.

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Notes:

Available from U.S. Department of Commerce, Office of Technical Services, Washington, D.C.

Referenced by:

2nd item, §9.8(iv).

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Staudt and arithmetical properties of Bernoulli numbers. Historia Sci. (2) 5 (1), pp. 69–74.

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External Links:

ISSN 0285-4821, MathReview (Peter M. Neumann), ZentralBlatt

Referenced by:

§24.10(ii).

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About von Staudt congruences for Bernoulli numbers. Comment. Math. Univ. St. Paul. 48 (2), pp. 137–144.

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External Links:

ISSN 0010-258X, MathReview (Arnold M. Adelberg), ZentralBlatt

Referenced by:

§24.10(ii).

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On the generalized Bernoulli numbers that belong to unequal characters. Rev. Mat. Iberoamericana 16 (3), pp. 459–475.

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External Links:

ISSN 0213-2230, MathReview (Aichi Kudo), ZentralBlatt

Referenced by:

§24.4(iii).

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14: 24.15 Related Sequences of Numbers

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§24.15(i) Genocchi Numbers

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§24.15(ii) Tangent Numbers

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§24.15(iii) Stirling Numbers

►The Stirling numbers of the first kind $s(n,m)$, and the second kind $S(n,m)$, are as defined in §26.8(i). … ►

§24.15(iv) Fibonacci and Lucas Numbers

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15: Bibliography I

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Centre for Experimental and Constructive Mathematics, Simon Fraser University, Canada.

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Notes:

From a decimal approximation, find the most likely exact value.

External Links:

Inverse Symbolic Calculator

Referenced by:

3rd item.

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A Classical Introduction to Modern Number Theory. 2nd edition, Springer-Verlag, New York.

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External Links:

ISBN 0-387-97329-X, MathReview (Glenn Stevens), ZentralBlatt

Referenced by:

§24.10(i), §24.10(ii), §24.10(iii), §24.17(iii).

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16: 18.39 Applications in the Physical Sciences

… ►This indicates that the Laguerre polynomials appearing in (18.39.29) are not classical OP’s, and in fact, even though infinite in number for fixed $l$, do not form a complete set. … ►

b) The Bohr Quantum Number

… ►where $n$ is now the Bohr Principle Quantum Number. … ►The solution, (18.39.29), of the spherical radial equation (18.39.28), now expressed in terms of the Bohr quantum number $n$, is … ►For applications of Legendre polynomials in fluid dynamics to study the flow around the outside of a puff of hot gas rising through the air, see Paterson (1983). …

17: 26.13 Permutations: Cycle Notation

… ►The Stirling cycle numbers of the first kind, denoted by $\left[\genfrac{}{}{0.0pt}{}{n}{k}\right]$, count the number of permutations of $\{1,2,\mathrm{\dots },n\}$ with exactly $k$ cycles. They are related to Stirling numbers of the first kind by …See §26.8 for generating functions, recurrence relations, identities, and asymptotic approximations. … ►The derangement number, $d(n)$, is the number of elements of ${𝔖}_n$ with no fixed points: … ►A permutation is even or odd according to the parity of the number of transpositions. …

18: Bibliography N

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The Development of Prime Number Theory: From Euclid to Hardy and Littlewood. Springer-Verlag, Berlin.

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External Links:

ISBN 3-540-66289-8, MathReview (D. R. Heath-Brown), ZentralBlatt

Referenced by:

§27.12.

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Coulomb Functions for Large Values of the Parameter $\eta$ . Technical report Atomic Energy of Canada Limited, Chalk River, Ontario.

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Notes:

Rep. CRT-526

External Links:

MathReview (A. Erdélyi)

Referenced by:

§33.7.

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An Introduction to the Theory of Numbers. 5th edition, John Wiley & Sons Inc., New York.

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External Links:

ISBN 0-471-62546-9, MathReview, ZentralBlatt

Referenced by:

Ch.27.

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Notes:

References and links to software for factorization and primality testing.

External Links:

Home Page

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6th item.

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19: Bibliography J

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Stirling Numbers, Lambert W and the Gamma Function. In Mathematical Aspects of Computer and Information Sciences, J. Blömer, I. S. Kotsireas, T. Kutsia, and D. E. Simos (Eds.), Cham, pp. 275–279.

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External Links:

ISBN 978-3-319-72453-9, ZentralBlatt

Referenced by:

§4.13.

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REMES2 — a Fortran program to calculate rational minimax approximations to a given function. Technical Report Technical Report AECL-4210, Atomic Energy of Canada Limited. Chalk River Nuclear Laboratories, Chalk River, Ontario.

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Referenced by:

§3.11(iii).

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20: 24.16 Generalizations

§24.16 Generalizations

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Polynomials and Numbers of Integer Order

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Bernoulli Numbers of the Second Kind

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Degenerate Bernoulli Numbers

… ►Here $s(n,m)$ again denotes the Stirling number of the first kind. …