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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: Bibliography O
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Studies on the Painlevé equations. II. Fifth Painlevé equation
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Japan. J. Math. (N.S.) 13 (1), pp. 47–76.
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Connection formulas for second-order differential equations having an arbitrary number of turning points of arbitrary multiplicities.
SIAM J. Math. Anal. 8 (4), pp. 673–700.
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Formulae and Tables, The Modified Quotients of Cylinder Functions.
Technical report
Technical Report UDC 517.564.3:518.25, Vol. 4, Report of the Institute of Industrial Science, University of Tokyo, Institute of Industrial Science, Chiba City, Japan.
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3: Bibliography N
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Toda equation and its solutions in special functions.
J. Phys. Soc. Japan 65 (6), pp. 1589–1597.
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The Development of Prime Number Theory: From Euclid to Hardy and Littlewood.
Springer-Verlag, Berlin.
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An Introduction to the Theory of Numbers.
5th edition, John Wiley & Sons Inc., New York.
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4: Bibliography Y
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Computation of Kummer functions for large argument by using the -method.
Trans. Inform. Process. Soc. Japan 36 (10), pp. 2335–2342 (Japanese).
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5: Guide to Searching the DLMF
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term:
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phrase:
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proximity operator:
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a textual word, a number, or a math symbol.
any double-quoted sequence of textual words and numbers.
adj, prec/n, and near/n, where n is any positive natural number.
$ |
stands for any number of alphanumeric characters |
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(the more conventional * is reserved for the multiplication operator) |
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6: 1.2 Elementary Algebra
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►The arithmetic mean of
numbers
is
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►The geometric mean
and harmonic mean
of positive numbers
are given by
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►If is a nonzero real number, then the weighted mean
of nonnegative numbers
, and positive numbers
with
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►The dot product notation is reserved for the physical three-dimensional vectors of (1.6.2).
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►The diagonal elements are not necessarily distinct, and the number of identical (degenerate) diagonal elements is the multiplicity of that specific eigenvalue.
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7: 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).