Emirates stirlingses Reservation Number 83267
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11: 24.16 Generalizations
§24.16 Generalizations
… ►Polynomials and Numbers of Integer Order
… ►Bernoulli Numbers of the Second Kind
… ►Degenerate Bernoulli Numbers
… ►Here again denotes the Stirling number of the first kind. …12: 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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13: 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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14: 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, . …15: 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).
16: 26.6 Other Lattice Path Numbers
§26.6 Other Lattice Path Numbers
… ►Delannoy Number
… ►Motzkin Number
… ►Narayana Number
… ►§26.6(iv) Identities
…17: 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
…18: 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
…19: 26.7 Set Partitions: Bell Numbers
§26.7 Set Partitions: Bell Numbers
►§26.7(i) Definitions
… ►§26.7(ii) Generating Function
… ►§26.7(iii) Recurrence Relation
… ►§26.7(iv) Asymptotic Approximation
…20: 24.19 Methods of Computation
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