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31—40 of 223 matching pages
31: 24.9 Inequalities
32: 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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33: 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 . …34: 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 … ►No sequel to Lehmer (1941) exists to date, but many tables of functions of number theory are included in Unpublished Mathematical Tables (1944).35: 24.4 Basic Properties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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§24.4(ix) Relations to Other Functions
►For the relation of Bernoulli numbers to the Riemann zeta function see §25.6, and to the Eulerian numbers see (26.14.11).36: 24.2 Definitions and Generating Functions
§24.2 Definitions and Generating Functions
►§24.2(i) Bernoulli Numbers and Polynomials
… ►§24.2(ii) Euler Numbers and Polynomials
… ► …37: 27.14 Unrestricted Partitions
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►Euler’s pentagonal number theorem states that
…where the exponents , , , , , , are the pentagonal numbers, defined by
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►For example, the Ramanujan identity
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§27.14(vi) Ramanujan’s Tau Function
… ►38: How to Cite
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►If you mention a specific equation (or chapter, section, …), you’ll help your readers find it by using our Permalinks & Reference numbers.
…produces pdf with the equation and table numbers linking directly into the DLMF website:
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