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21: 12.11 Zeros
§12.11(i) Distribution of Real Zeros
22: 19.33 Triaxial Ellipsoids
§19.33(iv) Self-Energy of an Ellipsoidal Distribution
Ellipsoidal distributions of charge or mass are used to model certain atomic nuclei and some elliptical galaxies. …In suitable units the self-energy of the distribution is given by …
23: Bibliography J
  • A. T. James (1964) Distributions of matrix variates and latent roots derived from normal samples. Ann. Math. Statist. 35 (2), pp. 475–501.
  • N. L. Johnson, S. Kotz, and N. Balakrishnan (1994) Continuous Univariate Distributions. 2nd edition, Vol. I, John Wiley & Sons Inc., New York.
  • N. L. Johnson, S. Kotz, and N. Balakrishnan (1995) Continuous Univariate Distributions. 2nd edition, Vol. II, John Wiley & Sons Inc., New York.
  • 24: 25.16 Mathematical Applications
    §25.16(i) Distribution of Primes
    In studying the distribution of primes p x , Chebyshev (1851) introduced a function ψ ( x ) (not to be confused with the digamma function used elsewhere in this chapter), given by …
    25: 27.2 Functions
    27.2.1 n = r = 1 ν ( n ) p r a r ,
    Tables of primes (§27.21) reveal great irregularity in their distribution. …
    27.2.3 π ( x ) x ln x .
    26: Bibliography O
  • F. Oberhettinger (1990) Tables of Fourier Transforms and Fourier Transforms of Distributions. Springer-Verlag, Berlin.
  • A. M. Odlyzko (1987) On the distribution of spacings between zeros of the zeta function. Math. Comp. 48 (177), pp. 273–308.
  • K. Ono (2000) Distribution of the partition function modulo m . Ann. of Math. (2) 151 (1), pp. 293–307.
  • 27: Bibliography H
  • J. Hadamard (1896) Sur la distribution des zéros de la fonction ζ ( s ) et ses conséquences arithmétiques. Bull. Soc. Math. France 24, pp. 199–220 (French).
  • V. B. Headley and V. K. Barwell (1975) On the distribution of the zeros of generalized Airy functions. Math. Comp. 29 (131), pp. 863–877.
  • G. W. Hill (1970) Algorithm 395: Student’s t-distribution. Comm. ACM 13 (10), pp. 617–619.
  • G. W. Hill (1981) Algorithm 571: Statistics for von Mises’ and Fisher’s distributions of directions: I 1 ( x ) / I 0 ( x ) , I 1.5 ( x ) / I 0.5 ( x ) and their inverses [S14]. ACM Trans. Math. Software 7 (2), pp. 233–238.
  • 28: 7.3 Graphics
    See accompanying text
    Figure 7.3.4: | ( x ) | 2 , - 8 x 8 . …He observed that the intensity distribution is given by | ( x ) | 2 . Magnify
    29: 16.23 Mathematical Applications
    In Janson et al. (1993) limiting distributions are discussed for the sparse connected components of these graphs, and the asymptotics of three F 2 2 functions are applied to compute the expected value of the excess. …
    30: Philip J. Davis
    He also had a big influence on the development of the NBS Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (A&S), which became one of the most widely distributed and highly cited publications in NIST’s history. …