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1: 11.13 Methods of Computation
A comprehensive approach is to integrate the defining inhomogeneous differential equations (11.2.7) and (11.2.9) numerically, using methods described in §3.7. …
2: Publications
  • B. V. Saunders and Q. Wang (1999) Using Numerical Grid Generation to Facilitate 3D Visualization of Complicated Mathematical Functions, Technical Report NISTIR 6413 (November 1999), National Institute of Standards and Technology. PDF
  • 3: 2.11 Remainder Terms; Stokes Phenomenon
    §2.11(i) Numerical Use of Asymptotic Expansions
    The rest of this section is devoted to general methods for increasing this accuracy. …
    §2.11(vi) Direct Numerical Transformations
    However, direct numerical transformations need to be used with care. …For example, extrapolated values may converge to an accurate value on one side of a Stokes line (§2.11(iv)), and converge to a quite inaccurate value on the other.
    4: Barry I. Schneider
    He has authored or co-authored 140 refereed papers and books and has given numerous invited talks in the US and abroad. …
    5: 5.21 Methods of Computation
    Another approach is to apply numerical quadrature (§3.5) to the integral (5.9.2), using paths of steepest descent for the contour. …
    6: 21.2 Definitions
    For numerical purposes we use the scaled Riemann theta function θ ^ ( z | Ω ) , defined by (Deconinck et al. (2004)), …
    7: Bibliography L
  • J. L. López and N. M. Temme (2010a) Asymptotics and numerics of polynomials used in Tricomi and Buchholz expansions of Kummer functions. Numer. Math. 116 (2), pp. 269–289.
  • 8: 10.47 Definitions and Basic Properties
    §10.47(iii) Numerically Satisfactory Pairs of Solutions
    For (10.47.1) numerically satisfactory pairs of solutions are given by Table 10.2.1 with the symbols J , Y , H , and ν replaced by j , y , h , and n , respectively. For (10.47.2) numerically satisfactory pairs of solutions are i n ( 1 ) ( z ) and k n ( z ) in the right half of the z -plane, and i n ( 1 ) ( z ) and k n ( - z ) in the left half of the z -plane. …
    9: Bibliography G
  • A. Gil, J. Segura, and N. M. Temme (2003b) Computing special functions by using quadrature rules. Numer. Algorithms 33 (1-4), pp. 265–275.
  • 10: Mathematical Introduction
    In referring to the numerical tables and approximations we use notation typified by x = 0 ( .05 ) 1 , 8D or 8S. …