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1: Bibliography D
  • B. Deconinck and J. N. Kutz (2006) Computing spectra of linear operators using the Floquet-Fourier-Hill method. J. Comput. Phys. 219 (1), pp. 296–321.
  • B. Döring (1966) Complex zeros of cylinder functions. Math. Comp. 20 (94), pp. 215–222.
  • N. Dunford and J. T. Schwartz (1988) Linear operators. Part II. Wiley Classics Library, John Wiley & Sons, Inc., New York.
  • C. F. Dunkl (1989) Differential-difference operators associated to reflection groups. Trans. Amer. Math. Soc. 311 (1), pp. 167–183.
  • T. M. Dunster (1989) Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions. SIAM J. Math. Anal. 20 (3), pp. 744–760.
  • 2: Bibliography K
  • A. Khare and U. Sukhatme (2004) Connecting Jacobi elliptic functions with different modulus parameters. Pramana 63 (5), pp. 921–936.
  • T. H. Koornwinder (2006) Lowering and Raising Operators for Some Special Orthogonal Polynomials. In Jack, Hall-Littlewood and Macdonald Polynomials, Contemp. Math., Vol. 417, pp. 227–238.
  • T. H. Koornwinder (2015) Fractional integral and generalized Stieltjes transforms for hypergeometric functions as transmutation operators. SIGMA Symmetry Integrability Geom. Methods Appl. 11, pp. Paper 074, 22.
  • T. Koornwinder, A. Kostenko, and G. Teschl (2018) Jacobi polynomials, Bernstein-type inequalities and dispersion estimates for the discrete Laguerre operator. Adv. Math. 333, pp. 796–821.
  • C. Kormanyos (2011) Algorithm 910: a portable C++ multiple-precision system for special-function calculations. ACM Trans. Math. Software 37 (4), pp. Art. 45, 27.
  • 3: 14.30 Spherical and Spheroidal Harmonics
    Sometimes Y l , m ( θ , ϕ ) is denoted by i l 𝔇 l m ( θ , ϕ ) ; also the definition of Y l , m ( θ , ϕ ) can differ from (14.30.1), for example, by inclusion of a factor ( 1 ) m . …
    Parity Operation
    Here, in spherical coordinates, L 2 is the squared angular momentum operator: …and L z is the z component of the angular momentum operator
    14.30.13 L z = i ϕ ;
    4: 18.39 Applications in the Physical Sciences
    The fundamental quantum Schrödinger operator, also called the Hamiltonian, , is a second order differential operator of the form … Analogous to (18.39.7) the 3D Schrödinger operator is …where L 2 is the (squared) angular momentum operator (14.30.12). … Here tridiagonal representations of simple Schrödinger operators play a similar role. The radial operator (18.39.28) …