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1: 1.16 Distributions
§1.16(viii) Fourier Transforms of Special Distributions
2: 1.14 Integral Transforms
1.14.1 ( f ) ( x ) = f ( x ) = 1 2 π - f ( t ) e i x t d t .
3: Errata
  • Subsection 1.16(viii)

    An entire new Subsection 1.16(viii) Fourier Transforms of Special Distributions, was contributed by Roderick Wong.

  • 4: Foreword
    That 1046-page tome proved to be an invaluable reference for the many scientists and engineers who use the special functions of applied mathematics in their day-to-day work, so much so that it became the most widely distributed and most highly cited NIST publication in the first 100 years of the institution’s existence. …
    5: 1.1 Special Notation
    §1.1 Special Notation
    (For other notation see Notation for the Special Functions.)
    x , y

    real variables.

    f , g

    distribution.

    6: 3.8 Nonlinear Equations
    For fixed-point methods for computing zeros of special functions, see Segura (2002), Gil and Segura (2003), and Gil et al. (2007a, Chapter 7). For describing the distribution of complex zeros of solutions of linear homogeneous second-order differential equations by methods based on the Liouville–Green (WKB) approximation, see Segura (2013). …
    7: Frank W. J. Olver
    Olver joined NIST in 1961 after having been recruited by Milton Abramowitz to be the author of the Chapter “Bessel Functions of Integer Order” in the Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, a publication which went on to become the most widely distributed and most highly cited publication in NIST’s history. Olver was an applied mathematician of world renown, one of the most widely recognized contemporary scholars in the field of special functions. …, the behavior of solutions as the independent variable, or some parameter, tends to infinity, and in the study of the particular solutions of differential equations known as special functions (e. … His well-known book, Asymptotics and Special Functions, was reprinted in the AKP Classics Series by AK Peters, Wellesley, Massachusetts, in 1997. … In April 2011, NIST co-organized a conference on “Special Functions in the 21st Century: Theory & Application” which was dedicated to Olver. …
    8: Bibliography Z
  • R. Zanovello (1995) Numerical analysis of Struve functions with applications to other special functions. Ann. Numer. Math. 2 (1-4), pp. 199–208.
  • A. Zarzo, J. S. Dehesa, and R. J. Yañez (1995) Distribution of zeros of Gauss and Kummer hypergeometric functions. A semiclassical approach. Ann. Numer. Math. 2 (1-4), pp. 457–472.
  • S. Zhang and J. Jin (1996) Computation of Special Functions. John Wiley & Sons Inc., New York.
  • 9: Bibliography T
  • N. M. Temme (1995a) Asymptotics of zeros of incomplete gamma functions. Ann. Numer. Math. 2 (1-4), pp. 415–423.
  • 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.
  • Go. Torres-Vega, J. D. Morales-Guzmán, and A. Zúñiga-Segundo (1998) Special functions in phase space: Mathieu functions. J. Phys. A 31 (31), pp. 6725–6739.
  • C. A. Tracy and H. Widom (1994) Level-spacing distributions and the Airy kernel. Comm. Math. Phys. 159 (1), pp. 151–174.
  • C. Truesdell (1948) An Essay Toward a Unified Theory of Special Functions. Annals of Mathematics Studies, no. 18, Princeton University Press, Princeton, N.J..
  • 10: Bibliography B
  • J. Baik, P. Deift, and K. Johansson (1999) On the distribution of the length of the longest increasing subsequence of random permutations. J. Amer. Math. Soc. 12 (4), pp. 1119–1178.
  • J. S. Ball (2000) Automatic computation of zeros of Bessel functions and other special functions. SIAM J. Sci. Comput. 21 (4), pp. 1458–1464.
  • L. E. Ballentine and S. M. McRae (1998) Moment equations for probability distributions in classical and quantum mechanics. Phys. Rev. A 58 (3), pp. 1799–1809.
  • C. Bingham, T. Chang, and D. Richards (1992) Approximating the matrix Fisher and Bingham distributions: Applications to spherical regression and Procrustes analysis. J. Multivariate Anal. 41 (2), pp. 314–337.
  • J. Bustoz, M. E. H. Ismail, and S. K. Suslov (Eds.) (2001) Special Functions 2000: Current Perspective and Future Directions. NATO Science Series II: Mathematics, Physics and Chemistry, Vol. 30, Kluwer Academic Publishers, Dordrecht.