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11: 1.16 Distributions
1.16.30 D = ( 1 i x 1 , 1 i x 2 , , 1 i x n ) .
12: 19.31 Probability Distributions
§19.31 Probability Distributions
R G ( x , y , z ) and R F ( x , y , z ) occur as the expectation values, relative to a normal probability distribution in 2 or 3 , of the square root or reciprocal square root of a quadratic form. …§19.16(iii) shows that for n = 3 the incomplete cases of R F and R G occur when μ = - 1 / 2 and μ = 1 / 2 , respectively, while their complete cases occur when n = 2 . …
13: 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.
  • J. R. Herndon (1961a) Algorithm 55: Complete elliptic integral of the first kind. Comm. ACM 4 (4), pp. 180.
  • J. R. Herndon (1961b) Algorithm 56: Complete elliptic integral of the second kind. Comm. ACM 4 (4), pp. 180–181.
  • G. W. Hill (1970) Algorithm 395: Student’s t-distribution. Comm. ACM 13 (10), pp. 617–619.
  • 14: 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.
  • S. Okui (1974) Complete elliptic integrals resulting from infinite integrals of Bessel functions. J. Res. Nat. Bur. Standards Sect. B 78B (3), pp. 113–135.
  • S. Okui (1975) Complete elliptic integrals resulting from infinite integrals of Bessel functions. II. J. Res. Nat. Bur. Standards Sect. B 79B (3-4), pp. 137–170.
  • K. Ono (2000) Distribution of the partition function modulo m . Ann. of Math. (2) 151 (1), pp. 293–307.
  • 15: Bibliography F
  • FDLIBM (free C library)
  • H. E. Fettis and J. C. Caslin (1969) A Table of the Complete Elliptic Integral of the First Kind for Complex Values of the Modulus. Part I. Technical report Technical Report ARL 69-0172, Aerospace Research Laboratories, Office of Aerospace Research, Wright-Patterson Air Force Base, Ohio.
  • A. Fresnel (1818) Mémoire sur la diffraction de la lumière. Mém. de l’Académie des Sciences, pp. 247–382.
  • 16: Bibliography M
  • J. W. Meijer and N. H. G. Baken (1987) The exponential integral distribution. Statist. Probab. Lett. 5 (3), pp. 209–211.
  • J. N. Merner (1962) Algorithm 149: Complete elliptic integral. Comm. ACM 5 (12), pp. 605.
  • T. Morita (1978) Calculation of the complete elliptic integrals with complex modulus. Numer. Math. 29 (2), pp. 233–236.
  • 17: 1.17 Integral and Series Representations of the Dirac Delta
    In applications in physics and engineering, the Dirac delta distribution1.16(iii)) is historically and customarily replaced by the Dirac delta (or Dirac delta function) δ ( x ) . …