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principle of the argument

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1: 1.10 Functions of a Complex Variable
Phase (or Argument) Principle
2: Bibliography
  • A. Abramov (1960) Tables of ln Γ ( z ) for Complex Argument. Pergamon Press, New York.
  • G. Allasia and R. Besenghi (1991) Numerical evaluation of the Kummer function with complex argument by the trapezoidal rule. Rend. Sem. Mat. Univ. Politec. Torino 49 (3), pp. 315–327.
  • D. E. Amos (1985) A subroutine package for Bessel functions of a complex argument and nonnegative order. Technical Report Technical Report SAND85-1018, Sandia National Laboratories, Albuquerque, NM.
  • 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.
  • Arblib (C) Arb: A C Library for Arbitrary Precision Ball Arithmetic.
  • 3: Bibliography S
  • J. Segura and A. Gil (1998) Parabolic cylinder functions of integer and half-integer orders for nonnegative arguments. Comput. Phys. Comm. 115 (1), pp. 69–86.
  • B. W. Shore and D. H. Menzel (1968) Principles of Atomic Spectra. John Wiley & Sons Ltd., New York.
  • K. M. Siegel and F. B. Sleator (1954) Inequalities involving cylindrical functions of nearly equal argument and order. Proc. Amer. Math. Soc. 5 (3), pp. 337–344.
  • K. M. Siegel (1953) An inequality involving Bessel functions of argument nearly equal to their order. Proc. Amer. Math. Soc. 4 (6), pp. 858–859.
  • 4: Bibliography L
  • S. Lewanowicz (1985) Recurrence relations for hypergeometric functions of unit argument. Math. Comp. 45 (172), pp. 521–535.
  • S. Lewanowicz (1987) Corrigenda: “Recurrence relations for hypergeometric functions of unit argument” [Math. Comp. 45 (1985), no. 172, 521–535; MR 86m:33004]. Math. Comp. 48 (178), pp. 853.
  • L.-W. Li, M. Leong, T.-S. Yeo, P.-S. Kooi, and K.-Y. Tan (1998a) Computations of spheroidal harmonics with complex arguments: A review with an algorithm. Phys. Rev. E 58 (5), pp. 6792–6806.
  • L. Lorch (1992) On Bessel functions of equal order and argument. Rend. Sem. Mat. Univ. Politec. Torino 50 (2), pp. 209–216 (1993).
  • H. A. Lorentz, A. Einstein, H. Minkowski, and H. Weyl (1923) The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity. Methuen and Co., Ltd., London.