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21—27 of 27 matching pages

21: Bibliography M
  • L. C. Maximon (2003) The dilogarithm function for complex argument. Proc. Roy. Soc. London Ser. A 459, pp. 2807–2819.
  • Fr. Mechel (1966) Calculation of the modified Bessel functions of the second kind with complex argument. Math. Comp. 20 (95), pp. 407–412.
  • J. Miller and V. S. Adamchik (1998) Derivatives of the Hurwitz zeta function for rational arguments. J. Comput. Appl. Math. 100 (2), pp. 201–206.
  • R. Morris (1979) The dilogarithm function of a real argument. Math. Comp. 33 (146), pp. 778–787.
  • C. Mortici (2013b) Further improvements of some double inequalities for bounding the gamma function. Math. Comput. Modelling 57 (5-6), pp. 1360–1363.
  • 22: 25.6 Integer Arguments
    §25.6 Integer Arguments
    §25.6(i) Function Values
    25.6.7 ζ ( 2 ) = 0 1 0 1 1 1 - x y d x d y .
    §25.6(ii) Derivative Values
    23: Bibliography H
  • P. I. Hadži (1976b) Integrals that contain a probability function of complicated arguments. Bul. Akad. Štiince RSS Moldoven. 1976 (1), pp. 80–84, 96 (Russian).
  • C. S. Herz (1955) Bessel functions of matrix argument. Ann. of Math. (2) 61 (3), pp. 474–523.
  • I. D. Hill (1973) Algorithm AS66: The normal integral. Appl. Statist. 22 (3), pp. 424–427.
  • M. Hiyama and H. Nakamura (1997) Two-center Coulomb functions. Comput. Phys. Comm. 103 (2-3), pp. 209–216.
  • 24: 3.5 Quadrature
    A second example is provided in Gil et al. (2001), where the method of contour integration is used to evaluate Scorer functions of complex argument9.12). …
    3.5.47 1 π h 2 D f ( x , y ) d x d y = j = 1 n w j f ( x j , y j ) + R ,
    3.5.48 1 4 h 2 S f ( x , y ) d x d y = j = 1 n w j f ( x j , y j ) + R .
    25: 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.
  • G. F. Remenets (1973) Computation of Hankel (Bessel) functions of complex index and argument by numerical integration of a Schläfli contour integral. Ž. Vyčisl. Mat. i Mat. Fiz. 13, pp. 1415–1424, 1636.
  • S. R. Rengarajan and J. E. Lewis (1980) Mathieu functions of integral orders and real arguments. IEEE Trans. Microwave Theory Tech. 28 (3), pp. 276–277.
  • D. St. P. Richards (2004) Total positivity properties of generalized hypergeometric functions of matrix argument. J. Statist. Phys. 116 (1-4), pp. 907–922.
  • 26: 2.11 Remainder Terms; Stokes Phenomenon
    However, on combining (2.11.6) with the connection formula (8.19.18), with m = 1 , we derive … For large | z | , with | ph z | 3 2 π - δ ( < 3 2 π ), the Whittaker function of the second kind has the asymptotic expansion (§13.19) … For example, using double precision d 20 is found to agree with (2.11.31) to 13D. …
    27: 34.4 Definition: 6 j Symbol
    The 6 j symbol is defined by the following double sum of products of 3 j symbols: … where the summation is over all nonnegative integers s such that the arguments in the factorials are nonnegative. … For alternative expressions for the 6 j symbol, written either as a finite sum or as other terminating generalized hypergeometric series F 3 4 of unit argument, see Varshalovich et al. (1988, §§9.2.1, 9.2.3).