winding number
(0.001 seconds)
1—10 of 223 matching pages
1: 24.1 Special Notation
…
►
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: 1.9 Calculus of a Complex Variable
…
►
§1.9(i) Complex Numbers
… ►Powers
… ►Winding Number
… ►where is an integer called the winding number of with respect to . If is simple and oriented in the positive rotational sense, then is or depending whether is inside or outside . …3: 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, . …4: 26.11 Integer Partitions: Compositions
…
►
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 .
…
►
26.11.1
…
►The Fibonacci numbers are determined recursively by
…
►Additional information on Fibonacci numbers can be found in Rosen et al. (2000, pp. 140–145).
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
…
►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:
…
►
►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.
…
►