rotation of argument
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1: 22.6 Elementary Identities
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§22.6(iv) Rotation of Argument (Jacobi’s Imaginary Transformation)
…2: 4.29 Graphics
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§4.29(i) Real Arguments
… ► ►§4.29(ii) Complex Arguments
►The conformal mapping is obtainable from Figure 4.15.7 by rotating both the -plane and the -plane through an angle , compare (4.28.8). …3: 16.24 Physical Applications
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►The symbols, or Clebsch–Gordan coefficients, play an important role in the decomposition of reducible representations of the rotation group into irreducible representations.
They can be expressed as functions with unit argument.
…These are balanced functions with unit argument.
Lastly, special cases of the symbols are functions with unit argument.
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4: Bibliography B
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New tables of Bessel functions of complex argument.
Comput. Math. Math. Phys. 37 (12), pp. 1480–1482.
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A program for computing the Riemann zeta function for complex argument.
Comput. Phys. Comm. 20 (3), pp. 441–445.
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Evaluation of the incomplete gamma function of imaginary argument by Chebyshev polynomials.
Math. Comp. 15 (73), pp. 7–11.
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Generalized hypergeometric functions at unit argument.
Proc. Amer. Math. Soc. 114 (1), pp. 145–153.
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Spectroscopy of Molecular Rotation in Gases and Liquids.
Cambridge University Press, Cambridge.
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5: Bibliography T
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Rotating black holes: Separable wave equations for gravitational and electromagnetic perturbations.
Phys. Rev. Lett. 29 (16), pp. 1114–1118.
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Erratum to “COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments”.
Comput. Phys. Comm. 159 (3), pp. 241–242.
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Algorithm 926: incomplete gamma functions with negative arguments.
ACM Trans. Math. Software 39 (2), pp. Art. 14, 9.
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Angular Momentum: An Illustrated Guide to Rotational Symmetries for Physical Systems.
A Wiley-Interscience Publication, John Wiley & Sons Inc., New York.
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Evaluation of the exponential integral for large complex arguments.
J. Research Nat. Bur. Standards 52, pp. 313–317.
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6: 33.22 Particle Scattering and Atomic and Molecular Spectra
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►The Coulomb functions given in this chapter are most commonly evaluated for real values of , , , and nonnegative integer values of , but they may be continued analytically to complex arguments and order as indicated in §33.13.
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Eigenstates using complex-rotated coordinates , so that resonances have square-integrable eigenfunctions. See for example Halley et al. (1993).
7: Bibliography K
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Algorithm 877: A subroutine package for cylindrical functions of complex order and nonnegative argument.
ACM Trans. Math. Software 34 (4), pp. Art. 22, 21.
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Algorithm 912: a module for calculating cylindrical functions of complex order and complex argument.
ACM Trans. Math. Software 37 (4), pp. Art. 47, 25.
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The efficient evaluation of the hypergeometric function of a matrix argument.
Math. Comp. 75 (254), pp. 833–846.
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Programs for computing the logarithm of the gamma function, and the digamma function, for complex argument.
Comput. Phys. Comm. 4, pp. 221–226.
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Sur le problème de la rotation d’un corps solide autour d’un point fixe.
Acta Math. 12 (1), pp. 177–232 (French).
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8: 22.19 Physical Applications
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22.19.2
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22.19.3
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►The classical rotation of rigid bodies in free space or about a fixed point may be described in terms of elliptic, or hyperelliptic, functions if the motion is integrable (Audin (1999, Chapter 1)).
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9: DLMF Project News
error generating summary10: Bibliography P
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On two-sided estimates, uniform with respect to the real argument and index, for modified Bessel functions.
Mat. Zametki 65 (5), pp. 681–692 (Russian).
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Exactification of the method of steepest descents: The Bessel functions of large order and argument.
Proc. Roy. Soc. London Ser. A 460, pp. 2737–2759.
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A new basis for the representation of the rotation group. Lamé and Heun polynomials.
J. Mathematical Phys. 14 (8), pp. 1130–1139.
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