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11: 7.14 Integrals
Fourier Transform
12: 24.19 Methods of Computation
  • A method related to “Stickelberger codes” is applied in Buhler et al. (2001); in particular, it allows for an efficient search for the irregular pairs ( 2 n , p ) . Discrete Fourier transforms are used in the computations. See also Crandall (1996, pp. 120–124).

  • 13: 13.10 Integrals
    §13.10(iv) Fourier Transforms
    For additional Fourier transforms see Erdélyi et al. (1954a, §§1.14, 2.14, 3.3) and Oberhettinger (1990, §§1.22, 2.22). …
    14: Bibliography O
  • F. Oberhettinger (1990) Tables of Fourier Transforms and Fourier Transforms of Distributions. Springer-Verlag, Berlin.
  • 15: 13.23 Integrals
    §13.23(ii) Fourier Transforms
    For additional Fourier transforms see Erdélyi et al. (1954a, §§1.14, 2.14, 3.3) and Oberhettinger (1990, §§1.22, 2.22). …
    16: Bibliography V
  • C. Van Loan (1992) Computational Frameworks for the Fast Fourier Transform. Frontiers in Applied Mathematics, Vol. 10, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
  • 17: 1.15 Summability Methods
    1.15.36 h ( x , y ) = 1 2 π - e - y | t | e - i x t F ( t ) d t ,
    where F ( t ) is the Fourier transform of f ( x ) 1.14(i)). …
    1.15.44 σ R ( θ ) = 1 2 π - R R ( 1 - | t | R ) e - i θ t F ( t ) d t ,
    18: Bibliography W
  • R. Wong and J. F. Lin (1978) Asymptotic expansions of Fourier transforms of functions with logarithmic singularities. J. Math. Anal. Appl. 64 (1), pp. 173–180.
  • 19: Bibliography S
  • O. A. Sharafeddin, H. F. Bowen, D. J. Kouri, and D. K. Hoffman (1992) Numerical evaluation of spherical Bessel transforms via fast Fourier transforms. J. Comput. Phys. 100 (2), pp. 294–296.
  • R. S. Strichartz (1994) A Guide to Distribution Theory and Fourier Transforms. Studies in Advanced Mathematics, CRC Press, Boca Raton, FL.
  • 20: Bibliography Z
  • Ya. M. Zhileĭkin and A. B. Kukarkin (1995) A fast Fourier-Bessel transform algorithm. Zh. Vychisl. Mat. i Mat. Fiz. 35 (7), pp. 1128–1133 (Russian).