About the Project

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1: Philip J. Davis
Davis joined the Section as part of a distinguished group of researchers studying mathematical methods for exploiting the new computational power. … After receiving an overview of the project and watching a short demo that included a few preliminary colorful, but static, 3D graphs constructed for the first Chapter, “Airy and Related Functions”, written by Olver, Davis expressed the hope that designing a web-based resource would allow the team to incorporate interesting computer graphics, such as function surfaces that could be rotated and examined. … DLMF users can rotate, rescale, zoom and otherwise explore mathematical function surfaces. …
2: 16.24 Physical Applications
The 3 j symbols, or Clebsch–Gordan coefficients, play an important role in the decomposition of reducible representations of the rotation group into irreducible representations. …
3: Bibliography K
  • E. G. Kalnins, W. Miller, and P. Winternitz (1976) The group O ( 4 ) , separation of variables and the hydrogen atom. SIAM J. Appl. Math. 30 (4), pp. 630–664.
  • C. Kassel (1995) Quantum Groups. Graduate Texts in Mathematics, Vol. 155, Springer-Verlag, New York.
  • T. H. Koornwinder (1984a) Jacobi Functions and Analysis on Noncompact Semisimple Lie Groups. In Special Functions: Group Theoretical Aspects and Applications, pp. 1–85.
  • T. H. Koornwinder (1994) Compact quantum groups and q -special functions. In Representations of Lie Groups and Quantum Groups, Pitman Res. Notes Math. Ser., Vol. 311, pp. 46–128.
  • S. Kowalevski (1889) Sur le problème de la rotation d’un corps solide autour d’un point fixe. Acta Math. 12 (1), pp. 177–232 (French).
  • 4: Bibliography P
  • 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.
  • R. Piessens (1982) Automatic computation of Bessel function integrals. Comput. Phys. Comm. 25 (3), pp. 289–295.
  • G. Pólya and R. C. Read (1987) Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds. Springer-Verlag, New York.
  • 5: 29.18 Mathematical Applications
    §29.18(iv) Other Applications
    Patera and Winternitz (1973) finds bases for the rotation group.
    6: Bibliography T
  • A. Terras (1999) Fourier Analysis on Finite Groups and Applications. London Mathematical Society Student Texts, Vol. 43, Cambridge University Press, Cambridge.
  • S. A. Teukolsky (1972) Rotating black holes: Separable wave equations for gravitational and electromagnetic perturbations. Phys. Rev. Lett. 29 (16), pp. 1114–1118.
  • 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.
  • C. L. Tretkoff and M. D. Tretkoff (1984) Combinatorial Group Theory, Riemann Surfaces and Differential Equations. In Contributions to Group Theory, Contemp. Math., Vol. 33, pp. 467–519.
  • 7: Bibliography B
  • G. Backenstoss (1970) Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.
  • A. O. Barut and L. Girardello (1971) New “coherent” states associated with non-compact groups. Comm. Math. Phys. 21 (1), pp. 41–55.
  • K. L. Bell and N. S. Scott (1980) Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.
  • W. G. Bickley (1935) Some solutions of the problem of forced convection. Philos. Mag. Series 7 20, pp. 322–343.
  • A. I. Burshtein and S. I. Temkin (1994) Spectroscopy of Molecular Rotation in Gases and Liquids. Cambridge University Press, Cambridge.
  • 8: 13.27 Mathematical Applications
    §13.27 Mathematical Applications
    Confluent hypergeometric functions are connected with representations of the group of third-order triangular matrices. The elements of this group are of the form …The other group elements correspond to integral operators whose kernels can be expressed in terms of Whittaker functions. … …
    9: 17.17 Physical Applications
    See Berkovich and McCoy (1998) and Bethuel (1998) for recent surveys. Quantum groups also apply q -series extensively. Quantum groups are really not groups at all but certain Hopf algebras. They were given this name because they play a role in quantum physics analogous to the role of Lie groups and special functions in classical mechanics. …
    10: 15.17 Mathematical Applications
    §15.17(iii) Group Representations
    Harmonic analysis can be developed for the Jacobi transform either as a generalization of the Fourier-cosine transform (§1.14(ii)) or as a specialization of a group Fourier transform. …
    §15.17(v) Monodromy Groups
    By considering, as a group, all analytic transformations of a basis of solutions under analytic continuation around all paths on the Riemann sheet, we obtain the monodromy group. These monodromy groups are finite iff the solutions of Riemann’s differential equation are all algebraic. …