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11: 20.14 Methods of Computation
The Fourier series of §20.2(i) usually converge rapidly because of the factors q ( n + 1 2 ) 2 or q n 2 , and provide a convenient way of calculating values of θ j ( z | τ ) . Similarly, their z -differentiated forms provide a convenient way of calculating the corresponding derivatives. …
12: Bibliography R
  • Yu. L. Ratis and P. Fernández de Córdoba (1993) A code to calculate (high order) Bessel functions based on the continued fractions method. Comput. Phys. Comm. 76 (3), pp. 381–388.
  • K. Reinsch and W. Raab (2000) Elliptic Integrals of the First and Second Kind – Comparison of Bulirsch’s and Carlson’s Algorithms for Numerical Calculation. In Special Functions (Hong Kong, 1999), C. Dunkl, M. Ismail, and R. Wong (Eds.), pp. 293–308.
  • S. O. Rice (1954) Diffraction of plane radio waves by a parabolic cylinder. Calculation of shadows behind hills. Bell System Tech. J. 33, pp. 417–504.
  • C. C. J. Roothaan and S. Lai (1997) Calculation of 3 n - j symbols by Labarthe’s method. International Journal of Quantum Chemistry 63 (1), pp. 57–64.
  • 13: 8.25 Methods of Computation
    A numerical inversion procedure is also given for calculating the value of x (with 10S accuracy), when a and P ( a , x ) are specified, based on Newton’s rule (§3.8(ii)). …
    14: 29.20 Methods of Computation
    The eigenvalues a ν m ( k 2 ) , b ν m ( k 2 ) , and the Lamé functions Ec ν m ( z , k 2 ) , Es ν m ( z , k 2 ) , can be calculated by direct numerical methods applied to the differential equation (29.2.1); see §3.7. …
    15: Bibliography J
  • D. Jacobs and F. Lambert (1972) On the numerical calculation of polylogarithms. Nordisk Tidskr. Informationsbehandling (BIT) 12 (4), pp. 581–585.
  • U. D. Jentschura and E. Lötstedt (2012) Numerical calculation of Bessel, Hankel and Airy functions. Computer Physics Communications 183 (3), pp. 506–519.
  • J. H. Johnson and J. M. Blair (1973) REMES2 — a Fortran program to calculate rational minimax approximations to a given function. Technical Report Technical Report AECL-4210, Atomic Energy of Canada Limited. Chalk River Nuclear Laboratories, Chalk River, Ontario.
  • 16: Bibliography S
  • R. P. Sagar (1991a) A Gaussian quadrature for the calculation of generalized Fermi-Dirac integrals. Comput. Phys. Comm. 66 (2-3), pp. 271–275.
  • C. W. Schelin (1983) Calculator function approximation. Amer. Math. Monthly 90 (5), pp. 317–325.
  • R. Spira (1971) Calculation of the gamma function by Stirling’s formula. Math. Comp. 25 (114), pp. 317–322.
  • A. Strecok (1968) On the calculation of the inverse of the error function. Math. Comp. 22 (101), pp. 144–158.
  • A. H. Stroud (1971) Approximate Calculation of Multiple Integrals. Prentice-Hall Inc., Englewood Cliffs, N.J..
  • 17: Bibliography B
  • A. Bar-Shalom and M. Klapisch (1988) NJGRAF: An efficient program for calculation of general recoupling coefficients by graphical analysis, compatible with NJSYM. Comput. Phys. Comm. 50 (3), pp. 375–393.
  • W. Bartky (1938) Numerical calculation of a generalized complete elliptic integral. Rev. Mod. Phys. 10, pp. 264–269.
  • R. Bulirsch (1965b) Numerical calculation of elliptic integrals and elliptic functions. Numer. Math. 7 (1), pp. 78–90.
  • R. Bulirsch (1967) Numerical calculation of the sine, cosine and Fresnel integrals. Numer. Math. 9 (5), pp. 380–385.
  • P. G. Burke (1970) A program to calculate a general recoupling coefficient. Comput. Phys. Comm. 1 (4), pp. 241–250.
  • 18: Bibliography F
  • D. F. Fang and J. F. Shriner (1992) A computer program for the calculation of angular-momentum coupling coefficients. Comput. Phys. Comm. 70 (1), pp. 147–153.
  • R. H. Farrell (1985) Multivariate Calculation. Use of the Continuous Groups. Springer Series in Statistics, Springer-Verlag, New York.
  • H. E. Fettis (1965) Calculation of elliptic integrals of the third kind by means of Gauss’ transformation. Math. Comp. 19 (89), pp. 97–104.
  • F. Feuillebois (1991) Numerical calculation of singular integrals related to Hankel transform. Comput. Math. Appl. 21 (2-3), pp. 87–94.
  • 19: Bibliography I
  • Inverse Symbolic Calculator (website) Centre for Experimental and Constructive Mathematics, Simon Fraser University, Canada.
  • 20: 25.10 Zeros
    Calculations relating to the zeros on the critical line make use of the real-valued function … Calculations based on the Riemann–Siegel formula reveal that the first ten billion zeros of ζ ( s ) in the critical strip are on the critical line (van de Lune et al. (1986)). …