numerical%20integration
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1—10 of 11 matching pages
1: Bibliography C
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Numerical computation of real or complex elliptic integrals.
Numer. Algorithms 10 (1-2), pp. 13–26.
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Numerical integration of related Hankel transforms by quadrature and continued fraction expansion.
Geophysics 48 (12), pp. 1671–1686.
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A method for numerical calculation of Fourier integrals.
Numer. Math. 8 (5), pp. 422–436.
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A method for numerical integration on an automatic copmputer.
Numer. Math. 2 (4), pp. 197–205.
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An encyclopaedia of cubature formulas.
J. Complexity 19 (3), pp. 445–453.
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2: Bibliography L
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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Numerical evaluation of integrals containing a spherical Bessel function by product integration.
J. Math. Phys. 22 (7), pp. 1399–1413.
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Asymptotics and numerics of polynomials used in Tricomi and Buchholz expansions of Kummer functions.
Numer. Math. 116 (2), pp. 269–289.
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Addendum to: “Changing the order of integration”.
J. Austral. Math. Soc. 14, pp. 383–384.
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Integrating some infinite oscillating tails.
J. Comput. Appl. Math. 12/13, pp. 109–117.
3: 18.40 Methods of Computation
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►Usually, however, other methods are more efficient, especially the numerical solution of difference equations (§3.6) and the application of uniform asymptotic expansions (when available) for OP’s of large degree.
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A numerical approach to the recursion coefficients and quadrature abscissas and weights
… ►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). …See Gautschi (1983) for examples of numerically stable and unstable use of the above recursion relations, and how one can then usefully differentiate between numerical results of low and high precision, as produced thereby. … ►Results of low ( to decimal digits) precision for are easily obtained for to . …4: Bibliography N
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On the numerical evaluation of the generalised Fermi-Dirac integrals.
Comput. Phys. Comm. 76 (1), pp. 48–50.
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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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Bisection hardly ever converges linearly.
Numer. Math. 70 (1), pp. 111–118.
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5: Bibliography D
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Methods of Numerical Integration.
2nd edition, Computer Science and Applied Mathematics, Academic Press Inc., Orlando, FL.
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On the computation of Mathieu functions.
J. Engrg. Math. 7, pp. 39–61.
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Texas Instruments, Inc..
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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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6: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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Numerical calculation of a generalized complete elliptic integral.
Rev. Mod. Phys. 10, pp. 264–269.
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Numerical Methods for Least Squares Problems.
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
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Numerical evaluation of continued fractions.
SIAM Rev. 6 (4), pp. 383–421.
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Numerical aspects of Mathieu eigenvalues.
Rend. Circ. Mat. Palermo (2) 15, pp. 51–97.
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7: 25.11 Hurwitz Zeta Function
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25.11.6
, , .
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25.11.7
, , , .
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25.11.30
, ,
►where the integration contour is a loop around the negative real axis as described for (25.5.20).
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8: Bibliography G
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Questions of Numerical Condition Related to Polynomials.
In Studies in Numerical Analysis, G. H. Golub (Ed.),
pp. 140–177.
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Computing complex Airy functions by numerical quadrature.
Numer. Algorithms 30 (1), pp. 11–23.
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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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Do integrable mappings have the Painlevé property?.
Phys. Rev. Lett. 67 (14), pp. 1825–1828.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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9: 6.16 Mathematical Applications
10: Bibliography M
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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Foundations of Finite Precision Rational Arithmetic.
In Fundamentals of Numerical Computation (Computer-oriented
Numerical Analysis), G. Alefeld and R. D. Grigorieff (Eds.),
Comput. Suppl., Vol. 2, Vienna, pp. 85–111.
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Numerical Methods for Roots of Polynomials. Part I.
Studies in Computational Mathematics, Vol. 14, Elsevier, Amsterdam.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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