Genocchi%20numbers
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21: 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, . …22: 26.12 Plane Partitions
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►Then the number of plane partitions in is
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►The number of symmetric plane partitions in is
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►The number of cyclically symmetric plane partitions in is
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►The number of descending plane partitions in is
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23: 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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24: 25.6 Integer Arguments
25: 25.11 Hurwitz Zeta Function
26: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Congruences of -adic integer order Bernoulli numbers.
J. Number Theory 59 (2), pp. 374–388.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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A Centennial History of the Prime Number Theorem.
In Number Theory,
Trends Math., pp. 1–14.
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27: 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
…28: Bibliography N
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The Development of Prime Number Theory: From Euclid to Hardy and Littlewood.
Springer-Verlag, Berlin.
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On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
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29: 26.8 Set Partitions: Stirling Numbers
§26.8 Set Partitions: Stirling Numbers
►§26.8(i) Definitions
… ► … ►§26.8(v) Identities
… ►§26.8(vi) Relations to Bernoulli Numbers
…30: 8 Incomplete Gamma and Related
Functions
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