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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: 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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3: 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).
4: 27.18 Methods of Computation: Primes
§27.18 Methods of Computation: Primes
►An overview of methods for precise counting of the number of primes not exceeding an arbitrary integer is given in Crandall and Pomerance (2005, §3.7). …An analytic approach using a contour integral of the Riemann zeta function (§25.2(i)) is discussed in Borwein et al. (2000). … ►These algorithms are used for testing primality of Mersenne numbers, , and Fermat numbers, . …5: 26.6 Other Lattice Path Numbers
§26.6 Other Lattice Path Numbers
… ►Delannoy Number
… ►Motzkin Number
… ►Narayana Number
… ►§26.6(iv) Identities
…6: 24.15 Related Sequences of Numbers
§24.15 Related Sequences of Numbers
►§24.15(i) Genocchi Numbers
… ►§24.15(ii) Tangent Numbers
… ►§24.15(iii) Stirling Numbers
… ►§24.15(iv) Fibonacci and Lucas Numbers
…7: 26.5 Lattice Paths: Catalan Numbers
§26.5 Lattice Paths: Catalan Numbers
►§26.5(i) Definitions
► is the Catalan number. … ►§26.5(ii) Generating Function
… ►§26.5(iii) Recurrence Relations
…8: 26.14 Permutations: Order Notation
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►As an example, is an element of The inversion number is the number of pairs of elements for which the larger element precedes the smaller:
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►The Eulerian number, denoted , is the number of permutations in with exactly descents.
…The Eulerian number
is equal to the number of permutations in with exactly excedances.
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§26.14(iii) Identities
…9: 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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