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11: Mathematical Introduction
In referring to the numerical tables and approximations we use notation typified by x = 0 ( .05 ) 1 , 8D or 8S. …
12: Marjorie A. McClain
 1956 in Ithaca, New York) is a mathematician in the Applied and Computational Mathematics Division of NIST where she has provided support for mathematical software libraries and assisted with numerical computing projects since 1979. More recently she has become an expert in the use of LaTeX and BibTex, and she has applied those skills in the preparation of the Latex documents for the DLMF chapters and in the development of the DLMF bibliography. …
13: Bibliography T
  • N. M. Temme (1978) The numerical computation of special functions by use of quadrature rules for saddle point integrals. II. Gamma functions, modified Bessel functions and parabolic cylinder functions. Report TW 183/78 Mathematisch Centrum, Amsterdam, Afdeling Toegepaste Wiskunde.
  • 14: 33.23 Methods of Computation
    Noble (2004) obtains double-precision accuracy for W η , μ ( 2 ρ ) for a wide range of parameters using a combination of recurrence techniques, power-series expansions, and numerical quadrature; compare (33.2.7). …
    15: 3.6 Linear Difference Equations
    §3.6 Linear Difference Equations
    §3.6(ii) Homogeneous Equations
    §3.6(iv) Inhomogeneous Equations
    16: Preface
    The DLMF will make full use of advanced communications and computational resources to present downloadable math data, manipulable graphs, tables of numerical values, and math-aware search. …
    17: Bibliography B
  • R. Barakat and E. Parshall (1996) Numerical evaluation of the zero-order Hankel transform using Filon quadrature philosophy. Appl. Math. Lett. 9 (5), pp. 21–26.
  • J. M. Borwein and I. J. Zucker (1992) Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind. IMA J. Numer. Anal. 12 (4), pp. 519–526.
  • 18: 28.34 Methods of Computation
  • (a)

    Direct numerical integration of the differential equation (28.2.1), with initial values given by (28.2.5) (§§3.7(ii), 3.7(v)).

  • (b)

    Use of asymptotic expansions and approximations for large q (§§28.8(i), 28.16). See also Zhang and Jin (1996, pp. 482–485).

  • (b)

    Use of asymptotic expansions and approximations for large q (§§28.8(ii)28.8(iv)).

  • (b)

    Direct numerical integration (§3.7) of the differential equation (28.20.1) for moderate values of the parameters.

  • (c)

    Use of asymptotic expansions for large z or large q . See §§28.25 and 28.26.

  • 19: 36.5 Stokes Sets
    20: Bibliography S
  • 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.