Emirates Airlines Reservation Number 832.615.6786
(0.002 seconds)
21—30 of 226 matching pages
21: 26.1 Special Notation
…
►
►
…
►Other notations for , the Stirling numbers of the first kind, include (Abramowitz and Stegun (1964, Chapter 24), Fort (1948)), (Jordan (1939), Moser and Wyman (1958a)), (Milne-Thomson (1933)), (Carlitz (1960), Gould (1960)), (Knuth (1992), Graham et al. (1994), Rosen et al. (2000)).
►Other notations for , the Stirling numbers of the second kind, include (Fort (1948)), (Jordan (1939)), (Moser and Wyman (1958b)), (Milne-Thomson (1933)), (Carlitz (1960), Gould (1960)), (Knuth (1992), Graham et al. (1994), Rosen et al. (2000)), and also an unconventional symbol in Abramowitz and Stegun (1964, Chapter 24).
binomial coefficient. | |
… | |
Eulerian number. | |
… | |
Bell number. | |
Catalan number. | |
… |
22: 27.3 Multiplicative Properties
§27.3 Multiplicative Properties
►Except for , , , and , the functions in §27.2 are multiplicative, which means and … ►
27.3.2
…
►
27.3.6
.
…
►
27.3.10
23: 27.1 Special Notation
§27.1 Special Notation
… ►positive integers (unless otherwise indicated). | |
… | |
prime numbers (or primes): integers () with only two positive integer divisors, and the number itself. | |
… | |
real numbers. | |
… |
24: 27.12 Asymptotic Formulas: Primes
§27.12 Asymptotic Formulas: Primes
… ►Prime Number Theorem
… ►The number of such primes not exceeding is … ►There are infinitely many Carmichael numbers.25: 27.2 Functions
…
►
§27.2(i) Definitions
… ►where are the distinct prime factors of , each exponent is positive, and is the number of distinct primes dividing . … ►(See Gauss (1863, Band II, pp. 437–477) and Legendre (1808, p. 394).) … ► … ►§27.2(ii) Tables
…26: 24.5 Recurrence Relations
§24.5 Recurrence Relations
… ►
24.5.3
,
…
►
24.5.5
►
§24.5(ii) Other Identities
… ►§24.5(iii) Inversion Formulas
…27: 24.6 Explicit Formulas
28: 27.13 Functions
…
►
§27.13(i) Introduction
►Whereas multiplicative number theory is concerned with functions arising from prime factorization, additive number theory treats functions related to addition of integers. …The subsections that follow describe problems from additive number theory. … ►§27.13(ii) Goldbach Conjecture
… ►§27.13(iii) Waring’s Problem
…29: 26.13 Permutations: Cycle Notation
…
►The Stirling cycle numbers of the first kind, denoted by , count the number of permutations of with exactly cycles.
They are related to Stirling numbers of the first kind by
…See §26.8 for generating functions, recurrence relations, identities, and asymptotic approximations.
…
►The derangement number, , is the number of elements of with no fixed points:
…
►A permutation is even or odd according to the parity of the number of transpositions.
…