for%20contour%20integrals
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5 matching pages
1: 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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An adaptive contour code for the numerical evaluation of the oscillatory cuspoid canonical integrals and their derivatives.
Computer Physics Comm. 132 (1-2), pp. 142–165.
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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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2: 3.4 Differentiation
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►If can be extended analytically into the complex plane, then from Cauchy’s integral formula (§1.9(iii))
…where is a simple closed contour described in the positive rotational sense such that and its interior lie in the domain of analyticity of , and is interior to .
…The integral on the right-hand side can be approximated by the composite trapezoidal rule (3.5.2).
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►The integral (3.4.18) becomes
…As explained in §§3.5(i) and 3.5(ix) the composite trapezoidal rule can be very efficient for computing integrals with analytic periodic integrands.
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3: Bibliography S
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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean.
SIAM J. Math. Anal. 20 (6), pp. 1514–1528.
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Computing the gamma function using contour integrals and rational approximations.
SIAM J. Numer. Anal. 45 (2), pp. 558–571.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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A Maple package for symmetric functions.
J. Symbolic Comput. 20 (5-6), pp. 755–768.
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Numerical Methods Based on Sinc and Analytic Functions.
Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
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4: Bibliography F
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
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Euler sums and contour integral representations.
Experiment. Math. 7 (1), pp. 15–35.
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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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5: Bibliography R
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On the definition and properties of generalized - symbols.
J. Math. Phys. 20 (12), pp. 2398–2415.
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Integral representations for products of Airy functions.
Z. Angew. Math. Phys. 46 (2), pp. 159–170.
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Integral representations for products of Airy functions. II. Cubic products.
Z. Angew. Math. Phys. 48 (4), pp. 646–655.
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Computation of Hankel (Bessel) functions of complex index and argument by numerical integration of a Schläfli contour integral.
Ž. Vyčisl. Mat. i Mat. Fiz. 13, pp. 1415–1424, 1636.
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Dawson’s integral and the sampling theorem.
Computers in Physics 3 (2), pp. 85–87.
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