About the Project

contour%20integrals

AdvancedHelp

(0.002 seconds)

5 matching pages

1: Bibliography K
  • R. B. Kearfott, M. Dawande, K. Du, and C. Hu (1994) Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.
  • M. K. Kerimov (1980) Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
  • N. P. Kirk, J. N. L. Connor, and C. A. Hobbs (2000) 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.
  • A. V. Kitaev and A. H. Vartanian (2004) Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I. Inverse Problems 20 (4), pp. 1165–1206.
  • T. H. Koornwinder (2009) The Askey scheme as a four-manifold with corners. Ramanujan J. 20 (3), pp. 409–439.
  • 2: 3.4 Differentiation
    If f can be extended analytically into the complex plane, then from Cauchy’s integral formula (§1.9(iii)) …where C is a simple closed contour described in the positive rotational sense such that C and its interior lie in the domain of analyticity of f , and x 0 is interior to C . …The integral on the right-hand side can be approximated by the composite trapezoidal rule (3.5.2). … 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. …
    3: Bibliography R
  • J. Raynal (1979) On the definition and properties of generalized 6 - j  symbols. J. Math. Phys. 20 (12), pp. 2398–2415.
  • W. H. Reid (1995) Integral representations for products of Airy functions. Z. Angew. Math. Phys. 46 (2), pp. 159–170.
  • W. H. Reid (1997a) Integral representations for products of Airy functions. II. Cubic products. Z. Angew. Math. Phys. 48 (4), pp. 646–655.
  • G. F. Remenets (1973) 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.
  • G. B. Rybicki (1989) Dawson’s integral and the sampling theorem. Computers in Physics 3 (2), pp. 85–87.
  • 4: Bibliography S
  • K. L. Sala (1989) Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean. SIAM J. Math. Anal. 20 (6), pp. 1514–1528.
  • T. Schmelzer and L. N. Trefethen (2007) Computing the gamma function using contour integrals and rational approximations. SIAM J. Numer. Anal. 45 (2), pp. 558–571.
  • A. Sharples (1967) Uniform asymptotic forms of modified Mathieu functions. Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
  • J. R. Stembridge (1995) A Maple package for symmetric functions. J. Symbolic Comput. 20 (5-6), pp. 755–768.
  • F. Stenger (1993) Numerical Methods Based on Sinc and Analytic Functions. Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
  • 5: Bibliography F
  • FDLIBM (free C library)
  • S. Fempl (1960) Sur certaines sommes des intégral-cosinus. Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
  • H. E. Fettis and J. C. Caslin (1964) 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.
  • H. E. Fettis (1970) On the reciprocal modulus relation for elliptic integrals. SIAM J. Math. Anal. 1 (4), pp. 524–526.
  • P. Flajolet and B. Salvy (1998) Euler sums and contour integral representations. Experiment. Math. 7 (1), pp. 15–35.