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1: 22.6 Elementary Identities
§22.6(ii) Double Argument
2: Bibliography T
  • I. J. Thompson and A. R. Barnett (1985) COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments. Comput. Phys. Comm. 36 (4), pp. 363–372.
  • I. J. Thompson and A. R. Barnett (1987) Modified Bessel functions I ν ( z ) and K ν ( z ) of real order and complex argument, to selected accuracy. Comput. Phys. Comm. 47 (2-3), pp. 245–257.
  • 3: Bibliography B
  • A. Bañuelos and R. A. Depine (1980) A program for computing the Riemann zeta function for complex argument. Comput. Phys. Comm. 20 (3), pp. 441–445.
  • A. R. Barnett (1982) COULFG: Coulomb and Bessel functions and their derivatives, for real arguments, by Steed’s method. Comput. Phys. Comm. 27, pp. 147–166.
  • K. H. Burrell (1974) Algorithm 484: Evaluation of the modified Bessel functions K0(Z) and K1(Z) for complex arguments. Comm. ACM 17 (9), pp. 524–526.
  • 4: Bibliography G
  • A. Gil and J. Segura (1997) Evaluation of Legendre functions of argument greater than one. Comput. Phys. Comm. 105 (2-3), pp. 273–283.
  • E. S. Ginsberg and D. Zaborowski (1975) Algorithm 490: The Dilogarithm function of a real argument [S22]. Comm. ACM 18 (4), pp. 200–202.
  • 5: Bibliography C
  • J. B. Campbell (1979) Bessel functions J ν ( x ) and Y ν ( x ) of real order and real argument. Comput. Phys. Comm. 18 (1), pp. 133–142.
  • J. B. Campbell (1981) Bessel functions I ν ( x ) and K ν ( x ) of real order and complex argument. Comput. Phys. Comm. 24 (1), pp. 97–105.
  • 6: Bibliography D
  • C. F. du Toit (1993) Bessel functions J n ( z ) and Y n ( z ) of integer order and complex argument. Comput. Phys. Comm. 78 (1-2), pp. 181–189.
  • 7: Bibliography K
  • P. Kravanja, O. Ragos, M. N. Vrahatis, and F. A. Zafiropoulos (1998) ZEBEC: A mathematical software package for computing simple zeros of Bessel functions of real order and complex argument. Comput. Phys. Comm. 113 (2-3), pp. 220–238.
  • 8: 35.10 Methods of Computation
    §35.10 Methods of Computation
    Other methods include numerical quadrature applied to double and multiple integral representations. See Yan (1992) for the F 1 1 and F 1 2 functions of matrix argument in the case m = 2 , and Bingham et al. (1992) for Monte Carlo simulation on O ( m ) applied to a generalization of the integral (35.5.8). …
    9: Bibliography
  • D. E. Amos (1986) Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order. ACM Trans. Math. Software 12 (3), pp. 265–273.
  • D. E. Amos (1990) Algorithm 683: A portable FORTRAN subroutine for exponential integrals of a complex argument. ACM Trans. Math. Software 16 (2), pp. 178–182.
  • 10: Bibliography N
  • M. Nardin, W. F. Perger, and A. Bhalla (1992a) Algorithm 707: CONHYP: A numerical evaluator of the confluent hypergeometric function for complex arguments of large magnitudes. ACM Trans. Math. Software 18 (3), pp. 345–349.