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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: Customize DLMF
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error generating summary4: George E. Andrews
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►An expert on -series, he is the author of
-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra.
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►Andrews was elected to the American Academy of Arts and Sciences in 1997, and to the National Academy of Sciences (USA) in 2003.
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5: Bibliography M
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Computational Algebra Group, School of Mathematics and Statistics, University of Sydney, Australia.
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Exceptional orthogonal polynomials.
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On the representation of numbers as a sum of squares.
Quarterly Journal of Math. 48, pp. 93–104.
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Asymptotic development of the Stirling numbers of the first kind.
J. London Math. Soc. 33, pp. 133–146.
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Stirling numbers of the second kind.
Duke Math. J. 25 (1), pp. 29–43.
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6: 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).