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1: 24.1 Special Notation
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Bernoulli Numbers and Polynomials
►The origin of the notation , , is not clear. … ►Euler Numbers and Polynomials
… ►Its coefficients were first studied in Euler (1755); they were called Euler numbers by Raabe in 1851. The notations , , as defined in §24.2(ii), were used in Lucas (1891) and Nörlund (1924). …2: Tom M. Apostol
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► 1923 in Helper, Utah, d.
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►He was internationally known for his textbooks on calculus, analysis, and analytic number theory, which have been translated into five languages, and for creating Project
MATHEMATICS!, a series of video programs that bring mathematics to life with computer animation, live action, music, and special effects.
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►In 1998, the Mathematical Association of America (MAA) awarded him the annual Trevor Evans Award, presented to authors of an exceptional article that is accessible to undergraduates, for his piece entitled “What Is the Most Surprising Result in Mathematics?” (Answer: the prime number theorem).
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3: Bibliography L
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A table of integrals involving the functions
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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Guide to Tables in the Theory of Numbers.
Bulletin of the National Research Council, No. 105, National Research Council, Washington, D.C..
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List of Prime Numbers from 1 to 10,006,721.
Publ. No. 165, Carnegie Institution of Washington, Washington, D.C..
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Highly accurate tables for elementary functions.
BIT 35 (3), pp. 352–360.
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4: 8.19 Generalized Exponential Integral
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►For ,
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8.19.15
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►For collections of integrals involving , especially for integer , see Apelblat (1983, §§7.1–7.2) and LeCaine (1945).
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5: 26.11 Integer Partitions: Compositions
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denotes the number of compositions of , and is the number of compositions into exactly
parts.
is the number of compositions of with no 1’s, where again .
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26.11.1
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►The Fibonacci numbers are determined recursively by
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►Additional information on Fibonacci numbers can be found in Rosen et al. (2000, pp. 140–145).