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11: Bibliography
  • J. C. Adams and P. N. Swarztrauber (1997) SPHEREPACK 2.0: A Model Development Facility. NCAR Technical Note Technical Report TN-436-STR, National Center for Atmospheric Research.
  • 12: Bibliography H
  • E. W. Hobson (1931) The Theory of Spherical and Ellipsoidal Harmonics. Cambridge University Press, London-New York.
  • 13: 15.17 Mathematical Applications
    §15.17(iii) Group Representations
    For harmonic analysis it is more natural to represent hypergeometric functions as a Jacobi function (§15.9(ii)). …First, as spherical functions on noncompact Riemannian symmetric spaces of rank one, but also as associated spherical functions, intertwining functions, matrix elements of SL ( 2 , ) , and spherical functions on certain nonsymmetric Gelfand pairs. 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. …
    14: Bibliography V
  • B. Ph. van Milligen and A. López Fraguas (1994) Expansion of vacuum magnetic fields in toroidal harmonics. Comput. Phys. Comm. 81 (1-2), pp. 74–90.
  • A. N. Vavreck and W. Thompson (1984) Some novel infinite series of spherical Bessel functions. Quart. Appl. Math. 42 (3), pp. 321–324.
  • 15: 18.39 Physical Applications
    For a harmonic oscillator, the potential energy is given by … when this is solved by separation of variables in spherical coordinates (§1.5(ii)). …
    16: Bibliography D
  • B. Davies (1973) Complex zeros of linear combinations of spherical Bessel functions and their derivatives. SIAM J. Math. Anal. 4 (1), pp. 128–133.
  • P. Dean (1966) The constrained quantum mechanical harmonic oscillator. Proc. Cambridge Philos. Soc. 62, pp. 277–286.
  • G. Delic (1979b) Chebyshev series for the spherical Bessel function j l ( r ) . Comput. Phys. Comm. 18 (1), pp. 73–86.