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11: Bibliography H
  • J. F. Hart, E. W. Cheney, C. L. Lawson, H. J. Maehly, C. K. Mesztenyi, J. R. Rice, H. G. Thacher, Jr., and C. Witzgall (1968) Computer Approximations. SIAM Ser. in Appl. Math., John Wiley & Sons Inc., New York.
  • C. Hastings (1955) Approximations for Digital Computers. Princeton University Press, Princeton, N.J..
  • E. J. Heller, W. P. Reinhardt, and H. A. Yamani (1973) On an “equivalent quadrature” calculation of matrix elements of ( z p 2 / 2 m ) 1 using an L 2 expansion technique. J. Comput. Phys. 13, pp. 536–550.
  • H. W. Hethcote (1970) Error bounds for asymptotic approximations of zeros of Hankel functions occurring in diffraction problems. J. Mathematical Phys. 11 (8), pp. 2501–2504.
  • 12: 18.38 Mathematical Applications
    §18.38(i) Classical OP’s: Numerical Analysis
    Approximation Theory
    For these results and applications in approximation theory see §3.11(ii) and Mason and Handscomb (2003, Chapter 3), Cheney (1982, p. 108), and Rivlin (1969, p. 31). … However, by using Hirota’s technique of bilinear formalism of soliton theory, Nakamura (1996) shows that a wide class of exact solutions of the Toda equation can be expressed in terms of various special functions, and in particular classical OP’s. …
    13: Bibliography K
  • R. P. Kanwal (1983) Generalized functions. Mathematics in Science and Engineering, Vol. 171, Academic Press, Inc., Orlando, FL.
  • D. Karp and S. M. Sitnik (2007) Asymptotic approximations for the first incomplete elliptic integral near logarithmic singularity. J. Comput. Appl. Math. 205 (1), pp. 186–206.
  • S. F. Khwaja and A. B. Olde Daalhuis (2012) Uniform asymptotic approximations for the Meixner-Sobolev polynomials. Anal. Appl. (Singap.) 10 (3), pp. 345–361.
  • U. J. Knottnerus (1960) Approximation Formulae for Generalized Hypergeometric Functions for Large Values of the Parameters. J. B. Wolters, Groningen.
  • V. I. Krylov and N. S. Skoblya (1985) A Handbook of Methods of Approximate Fourier Transformation and Inversion of the Laplace Transformation. Mir, Moscow.
  • 14: Bibliography B
  • M. V. Berry (1966) Uniform approximation for potential scattering involving a rainbow. Proc. Phys. Soc. 89 (3), pp. 479–490.
  • M. V. Berry (1969) Uniform approximation: A new concept in wave theory. Science Progress (Oxford) 57, pp. 43–64.
  • D. L. Bosley (1996) A technique for the numerical verification of asymptotic expansions. SIAM Rev. 38 (1), pp. 128–135.
  • C. Brezinski (1980) Padé-type Approximation and General Orthogonal Polynomials. International Series of Numerical Mathematics, Vol. 50, Birkhäuser Verlag, Basel.
  • J. D. Buckholtz (1963) Concerning an approximation of Copson. Proc. Amer. Math. Soc. 14 (4), pp. 564–568.