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31: 26.17 The Twelvefold Way
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►The twelvefold way gives the number of mappings from set of objects to set of objects (putting balls from set into boxes in set ).
…In this table is Pochhammer’s symbol, and and are defined in §§26.8(i) and 26.9(i).
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32: Bibliography F
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Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
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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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Faster computation of Bernoulli numbers.
J. Algorithms 13 (3), pp. 431–445.
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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.
33: 24.20 Tables
§24.20 Tables
… ►Wagstaff (1978) gives complete prime factorizations of and for and , respectively. …34: 24.9 Inequalities
35: 4.19 Maclaurin Series and Laurent Series
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►In (4.19.3)–(4.19.9), are the Bernoulli numbers and are the Euler numbers (§§24.2(i)–24.2(ii)).
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4.19.3
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4.19.4
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4.19.5
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4.19.6
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36: 27.16 Cryptography
§27.16 Cryptography
… ►The primes are kept secret but their product , an 800-digit number, is made public. …With the most efficient computer techniques devised to date (2010), factoring an 800-digit number may require billions of years on a single computer. For this reason, the codes are considered unbreakable, at least with the current state of knowledge on factoring large numbers. … ►Thus, and . …37: 27.21 Tables
§27.21 Tables
… ►Bressoud and Wagon (2000, pp. 103–104) supplies tables and graphs that compare , and . … ►Lehmer (1941) gives a comprehensive account of tables in the theory of numbers, including virtually every table published from 1918 to 1941. … ►No sequel to Lehmer (1941) exists to date, but many tables of functions of number theory are included in Unpublished Mathematical Tables (1944).38: 24.4 Basic Properties
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§24.4(iv) Finite Expansions
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24.4.15
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24.4.16
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