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21: 24.2 Definitions and Generating Functions
§24.2 Definitions and Generating Functions
►§24.2(i) Bernoulli Numbers and Polynomials
… ►§24.2(ii) Euler Numbers and Polynomials
… ► …22: 27.9 Quadratic Characters
§27.9 Quadratic Characters
►For an odd prime , the Legendre symbol is defined as follows. … ►
27.9.2
►If are distinct odd primes, then the quadratic reciprocity law states that
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►If an odd integer has prime factorization , then the Jacobi symbol
is defined by , with .
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23: 24.9 Inequalities
24: 24.11 Asymptotic Approximations
25: 26.9 Integer Partitions: Restricted Number and Part Size
§26.9 Integer Partitions: Restricted Number and Part Size
… ► denotes the number of partitions of into at most parts. See Table 26.9.1. … ►It follows that also equals the number of partitions of into parts that are less than or equal to . …26: 26.16 Multiset Permutations
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►Let be the multiset that has copies of , .
…The number of elements in is the multinomial coefficient (§26.4) .
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►The definitions of inversion number and major index can be extended to permutations of a multiset such as .
Thus , and
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►
26.16.1
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27: 26.3 Lattice Paths: Binomial Coefficients
…
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is the number of ways of choosing objects from a collection of distinct objects without regard to order.
is the number of lattice paths from to .
…The number of lattice paths from to , , that stay on or above the line is
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►
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28: 8 Incomplete Gamma and Related
Functions
Chapter 8 Incomplete Gamma and Related Functions
…29: Errata
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►This release increments the minor version number and contains considerable additions of new material and clarifications.
…
►These additions were facilitated by an extension of the scheme for reference numbers; with “_” introducing intermediate numbers.
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►
Table 26.8.1
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►
Chapters 8, 20, 36
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Version 1.0.11 (June 8, 2016)
… ►Originally the Stirling number was given incorrectly as 6327. The correct number is 63273.
10 |
Reported 2013-11-25 by Svante Janson.
30: 26.10 Integer Partitions: Other Restrictions
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►
denotes the number of partitions of into distinct parts.
denotes the number of partitions of into at most distinct parts.
denotes the number of partitions of into parts with difference at least .
… denotes the number of partitions of into odd parts.
denotes the number of partitions of into parts taken from the set .
…