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21: 10.42 Zeros
The distribution of the zeros of K n ( n z ) in the sector 3 2 π ph z 1 2 π in the cases n = 1 , 5 , 10 is obtained on rotating Figures 10.21.2, 10.21.4, 10.21.6, respectively, through an angle 1 2 π so that in each case the cut lies along the positive imaginary axis. …
22: 12.11 Zeros
§12.11(i) Distribution of Real Zeros
23: 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 …
24: Bibliography Z
  • 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.
  • A. H. Zemanian (1987) Distribution Theory and Transform Analysis, An Introduction and Generalized Functions with Applications. Dover, New York.
  • 25: 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 …
    26: 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 .
    27: 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.
  • 28: 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.
  • 29: 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
    30: 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. …