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11: Bibliography G
  • I. Gargantini and P. Henrici (1967) A continued fraction algorithm for the computation of higher transcendental functions in the complex plane. Math. Comp. 21 (97), pp. 1829.
  • W. Gautschi (1966) Algorithm 292: Regular Coulomb wave functions. Comm. ACM 9 (11), pp. 793–795.
  • W. Gautschi (1969) Algorithm 363: Complex error function. Comm. ACM 12 (11), pp. 635.
  • H. W. Gould (1960) Stirling number representation problems. Proc. Amer. Math. Soc. 11 (3), pp. 447–451.
  • V. I. Gromak (1975) Theory of Painlevé’s equations. Differ. Uravn. 11 (11), pp. 373–376 (Russian).
  • 12: 4.17 Special Values and Limits
    Table 4.17.1: Trigonometric functions: values at multiples of 1 12 π .
    θ sin θ cos θ tan θ csc θ sec θ cot θ
    11 π / 12 1 4 2 ( 3 1 ) 1 4 2 ( 3 + 1 ) ( 2 3 ) 2 ( 3 + 1 ) 2 ( 3 1 ) ( 2 + 3 )
    13: Bibliography L
  • D. Le (1985) An efficient derivative-free method for solving nonlinear equations. ACM Trans. Math. Software 11 (3), pp. 250–262.
  • A. Leitner and J. Meixner (1960) Eine Verallgemeinerung der Sphäroidfunktionen. Arch. Math. 11, pp. 29–39.
  • H. Lotsch and M. Gray (1964) Algorithm 244: Fresnel integrals. Comm. ACM 7 (11), pp. 660–661.
  • N. A. Lukaševič (1967b) On the theory of Painlevé’s third equation. Differ. Uravn. 3 (11), pp. 1913–1923 (Russian).
  • Y. L. Luke (1977a) Algorithms for rational approximations for a confluent hypergeometric function. Utilitas Math. 11, pp. 123–151.
  • 14: 1 Algebraic and Analytic Methods
    15: 14 Legendre and Related Functions
    16: 26.12 Plane Partitions
    Table 26.12.1: Plane partitions.
    n pp ( n ) n pp ( n ) n pp ( n )
    1 1 18 29601 35 416 91046
    11 859 28 24 83234 45 17740 79109
    12 1479 29 37 59612 46 25435 35902
    26.12.26 pp ( n ) ( ζ ( 3 ) ) 7 / 36 2 11 / 36 ( 3 π ) 1 / 2 n 25 / 36 exp ( 3 ( ζ ( 3 ) ) 1 / 3 ( 1 2 n ) 2 / 3 + ζ ( 1 ) ) ,
    17: 34.6 Definition: 9 j Symbol
    34.6.1 { j 11 j 12 j 13 j 21 j 22 j 23 j 31 j 32 j 33 } = all  m r s ( j 11 j 12 j 13 m 11 m 12 m 13 ) ( j 21 j 22 j 23 m 21 m 22 m 23 ) ( j 31 j 32 j 33 m 31 m 32 m 33 ) ( j 11 j 21 j 31 m 11 m 21 m 31 ) ( j 12 j 22 j 32 m 12 m 22 m 32 ) ( j 13 j 23 j 33 m 13 m 23 m 33 ) ,
    34.6.2 { j 11 j 12 j 13 j 21 j 22 j 23 j 31 j 32 j 33 } = j ( 1 ) 2 j ( 2 j + 1 ) { j 11 j 21 j 31 j 32 j 33 j } { j 12 j 22 j 32 j 21 j j 23 } { j 13 j 23 j 33 j j 11 j 12 } .
    18: Bibliography O
  • A. B. Olde Daalhuis (1998a) Hyperasymptotic solutions of higher order linear differential equations with a singularity of rank one. Proc. Roy. Soc. London Ser. A 454, pp. 1–29.
  • F. W. J. Olver (1964a) Error analysis of Miller’s recurrence algorithm. Math. Comp. 18 (85), pp. 65–74.
  • F. W. J. Olver (1974) Error bounds for stationary phase approximations. SIAM J. Math. Anal. 5 (1), pp. 19–29.
  • S. Olver (2011) Numerical solution of Riemann-Hilbert problems: Painlevé II. Found. Comput. Math. 11 (2), pp. 153–179.
  • H. Oser (1960) Algorithm 22: Riccati-Bessel functions of first and second kind. Comm. ACM 3 (11), pp. 600–601.
  • 19: Bibliography D
  • M. D’Ocagne (1904) Sur une classe de nombres rationnels réductibles aux nombres de Bernoulli. Bull. Sci. Math. (2) 28, pp. 29–32 (French).
  • P. Deift, T. Kriecherbauer, K. T.-R. McLaughlin, S. Venakides, and X. Zhou (1999b) Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory. Comm. Pure Appl. Math. 52 (11), pp. 1335–1425.
  • E. Dorrer (1968) Algorithm 322. F-distribution. Comm. ACM 11 (2), pp. 116–117.
  • B. A. Dubrovin (1981) Theta functions and non-linear equations. Uspekhi Mat. Nauk 36 (2(218)), pp. 11–80 (Russian).
  • J. Dutka (1981) The incomplete beta function—a historical profile. Arch. Hist. Exact Sci. 24 (1), pp. 1129.
  • 20: Bibliography K
  • G. A. Kalugin, D. J. Jeffrey, and R. M. Corless (2012) Bernstein, Pick, Poisson and related integral expressions for Lambert W . Integral Transforms Spec. Funct. 23 (11), pp. 817–829.
  • E. L. Kaplan (1948) Auxiliary table for the incomplete elliptic integrals. J. Math. Physics 27, pp. 11–36.
  • M. K. Kerimov and S. L. Skorokhodov (1987) On the calculation of the multiple complex roots of the derivatives of cylindrical Bessel functions. Zh. Vychisl. Mat. i Mat. Fiz. 27 (11), pp. 1628–1639, 1758.
  • R. P. Kerr (1963) Gravitational field of a spinning mass as an example of algebraically special metrics. Phys. Rev. Lett. 11 (5), pp. 237–238.
  • K. S. Kölbig (1968) Algorithm 327: Dilogarithm [S22]. Comm. ACM 11 (4), pp. 270–271.