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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: 34.6 Definition: Symbol
§34.6 Definition: Symbol
►The symbol may be defined either in terms of symbols or equivalently in terms of symbols: ►
34.6.1
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34.6.2
►The symbol may also be written as a finite triple sum equivalent to a terminating generalized hypergeometric series of three variables with unit arguments.
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3: 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.
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stands for any number of alphanumeric characters |
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(the more conventional * is reserved for the multiplication operator) |
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4: 26.6 Other Lattice Path Numbers
§26.6 Other Lattice Path Numbers
… ►Delannoy Number
… ►Motzkin Number
… ►Narayana Number
… ►§26.6(iv) Identities
…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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►The Fibonacci numbers are determined recursively by
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26.11.6
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►Additional information on Fibonacci numbers can be found in Rosen et al. (2000, pp. 140–145).
6: 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
…7: 16.7 Relations to Other Functions
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►For , , symbols see Chapter 34.
Further representations of special functions in terms of functions are given in Luke (1969a, §§6.2–6.3), and an extensive list of functions with rational numbers as parameters is given in Krupnikov and Kölbig (1997).
8: 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
…9: 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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