…
►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.
…
L. V. Babushkina, M. K. Kerimov, and A. I. Nikitin (1997)New tables of Bessel functions of complex argument.
Comput. Math. Math. Phys.37 (12), pp. 1480–1482.
ⓘ
Notes:
Russian original in Zh. Vychisl. Mat. i Mat. Fiz.
37(1997), no. 12, 1526–1528
S. A. Teukolsky (1972)Rotating black holes: Separable wave equations for gravitational and electromagnetic perturbations.
Phys. Rev. Lett.29 (16), pp. 1114–1118.
I. J. Thompson (2004)Erratum to “COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments”.
Comput. Phys. Comm.159 (3), pp. 241–242.
W. J. Thompson (1994)Angular Momentum: An Illustrated Guide to Rotational Symmetries for Physical Systems.
A Wiley-Interscience Publication, John Wiley & Sons Inc., New York.
ⓘ
Notes:
With 1 Macintosh floppy disk (3.5 inch; DD).
Programs for the calculation of symbols
are included.
…
►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.
…
►
•
Eigenstates using complex-rotated coordinates ,
so that resonances have square-integrable eigenfunctions. See for example
Halley et al. (1993).
M. Kodama (2008)Algorithm 877: A subroutine package for cylindrical functions of complex order and nonnegative argument.
ACM Trans. Math. Software34 (4), pp. Art. 22, 21.
M. Kodama (2011)Algorithm 912: a module for calculating cylindrical functions of complex order and complex argument.
ACM Trans. Math. Software37 (4), pp. Art. 47, 25.
K. S. Kölbig (1972c)Programs for computing the logarithm of the gamma function, and the digamma function, for complex argument.
Comput. Phys. Comm.4, pp. 221–226.
…
►►►Figure 22.19.1: Jacobi’s amplitude function for and .
When , increases monotonically indicating that the motion of the pendulum is unbounded in , corresponding to free rotation about the fulcrum; compare Figure 22.16.1.
…
Magnify
…
►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)).
…
B. V. Pal′tsev (1999)On two-sided estimates, uniform with respect to the real argument and index, for modified Bessel functions.
Mat. Zametki65 (5), pp. 681–692 (Russian).
ⓘ
Notes:
English translation in Math. Notes 65 (1999) pp. 571-581.
R. B. Paris (2004)Exactification of the method of steepest descents: The Bessel functions of large order and argument.
Proc. Roy. Soc. London Ser. A460, pp. 2737–2759.
J. Patera and P. Winternitz (1973)A new basis for the representation of the rotation group. Lamé and Heun polynomials.
J. Mathematical Phys.14 (8), pp. 1130–1139.