beta%20integrals
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11—16 of 16 matching pages
11: Bibliography G
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Algorithm 222: Incomplete beta function ratios.
Comm. ACM 7 (3), pp. 143–144.
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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules.
ACM Trans. Math. Software 20 (1), pp. 21–62.
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A table of integrals of the exponential integral.
J. Res. Nat. Bur. Standards Sect. B 73B, pp. 191–210.
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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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12: Bibliography K
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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The Askey scheme as a four-manifold with corners.
Ramanujan J. 20 (3), pp. 409–439.
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HYP and HYPQ. Mathematica packages for the manipulation of binomial sums and hypergeometric series respectively -binomial sums and basic hypergeometric series.
Séminaire Lotharingien de Combinatoire 30, pp. 61–76.
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13: 18.40 Methods of Computation
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►In what follows we consider only the simple, illustrative, case that is continuously differentiable so that , with real, positive, and continuous on a real interval The strategy will be to: 1) use the moments to determine the recursion coefficients of equations (18.2.11_5) and (18.2.11_8); then, 2) to construct the quadrature abscissas and weights (or Christoffel numbers) from the J-matrix of §3.5(vi), equations (3.5.31) and(3.5.32).
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►There are many ways to implement these first two steps, noting that the expressions for and of equation (18.2.30) are of little practical numerical value, see Gautschi (2004) and Golub and Meurant (2010).
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►Results of low ( to decimal digits) precision for are easily obtained for to .
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►Equation (18.40.7) provides step-histogram approximations to , as shown in Figure 18.40.1 for and , shown here for the repulsive Coulomb–Pollaczek OP’s of Figure 18.39.2, with the parameters as listed therein.
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►The example chosen is inversion from the for the weight function for the repulsive Coulomb–Pollaczek, RCP, polynomials of (18.39.50).
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14: Bibliography C
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Algorithm AS 310. Computing the non-central beta distribution function.
Appl. Statist. 46 (1), pp. 146–156.
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
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Integrals involving complete elliptic integrals.
J. Comput. Appl. Math. 106 (1), pp. 169–175.
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15: Errata
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Equations (31.3.10), (31.3.11)
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Paragraph Case III:
(in §22.19(ii))
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Chapters 8, 20, 36
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Equation (17.13.3)
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References
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31.3.10
31.3.11
In both equations, the second entry in the has been corrected with an extra minus sign.
Two corrections have been made in this paragraph. First, the correct range of the initial displacement is . Previously it was . Second, the correct period of the oscillations is . Previously it was given incorrectly as .
Reported 2014-05-02 by Svante Janson.
17.13.3
Originally the differential was identified incorrectly as ; the correct differential is .
Reported 2011-04-08.
16: Bibliography D
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Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire
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Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
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Algorithm 708: Significant digit computation of the incomplete beta function ratios.
ACM Trans. Math. Software 18 (3), pp. 360–373.
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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The incomplete beta function—a historical profile.
Arch. Hist. Exact Sci. 24 (1), pp. 11–29.
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