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1: 34.9 Graphical Method
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►For an account of this method see Brink and Satchler (1993, Chapter VII).
For specific examples of the graphical method of representing sums involving the , and symbols, see Varshalovich et al. (1988, Chapters 11, 12) and Lehman and O’Connell (1973, §3.3).
2: Bibliography L
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Eine Verallgemeinerung der Sphäroidfunktionen.
Arch. Math. 11, pp. 29–39.
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Evaluation of Bessel function integrals with algebraic singularities.
J. Comput. Appl. Math. 37 (1-3), pp. 101–112.
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Two index laws for fractional integrals and derivatives.
J. Austral. Math. Soc. 14, pp. 385–410.
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Bessel transforms and rational extrapolation.
Numer. Math. 47 (1), pp. 1–14.
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Integrating some infinite oscillating tails.
J. Comput. Appl. Math. 12/13, pp. 109–117.
3: Bibliography
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On the zeros of confluent hypergeometric functions. III. Characterization by means of nonlinear equations.
Lett. Nuovo Cimento (2) 29 (11), pp. 353–358.
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Some orthogonal -polynomials.
Math. Nachr. 30, pp. 47–61.
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Normal forms of functions in the neighborhood of degenerate critical points.
Uspehi Mat. Nauk 29 (2(176)), pp. 11–49 (Russian).
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Solid State Physics.
Holt, Rinehart and Winston, New York.
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Orthogonal Polynomials and Special Functions.
CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 21, Society for Industrial and Applied Mathematics, Philadelphia, PA.
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4: Bibliography I
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Computation of integrals over the half-line involving products of Bessel functions, with application to microwave transmission lines.
Z. Angew. Math. Mech. 75 (12), pp. 917–926.
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Highly Oscillatory Quadrature: The Story So Far.
In Numerical Mathematics and Advanced Applications, A. Bermudez de Castro and others (Eds.),
pp. 97–118.
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-Hermite polynomials, biorthogonal rational functions, and -beta integrals.
Trans. Amer. Math. Soc. 346 (1), pp. 63–116.
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Classical and Quantum Orthogonal Polynomials in One Variable.
Encyclopedia of Mathematics and its Applications, Vol. 98, Cambridge University Press, Cambridge.
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From Gauss to Painlevé: A Modern Theory of Special Functions.
Aspects of Mathematics E, Vol. 16, Friedr. Vieweg & Sohn, Braunschweig, Germany.
5: Bibliography E
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Angular Momentum in Quantum Mechanics.
3rd printing, with corrections, 2nd edition, Princeton University Press, Princeton, NJ.
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The numerical inversion of two classes of Kontorovich-Lebedev transform by direct quadrature.
J. Comput. Appl. Math. 61 (1), pp. 43–72.
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An upper bound for the zeros of the derivative of Bessel functions.
Rend. Circ. Mat. Palermo (2) 46 (1), pp. 123–130.
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A comparison of some methods for the evaluation of highly oscillatory integrals.
J. Comput. Appl. Math. 112 (1-2), pp. 55–69.
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The asymptotic behaviour of the inhomogeneous Airy function
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Math. Chronicle 12, pp. 99–104.
6: Bibliography G
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On high precision methods for computing integrals involving Bessel functions.
Math. Comp. 33 (147), pp. 1049–1057.
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On the generalization of a method for computing Bessel function integrals.
J. Comput. Appl. Math. 6 (2), pp. 167–168.
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The triplets of helium.
Philos. Trans. Roy. Soc. London Ser. A 228, pp. 151–196.
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Matrix Computations.
3rd edition, Johns Hopkins University Press, Baltimore, MD.
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Constructing wavefunctions for nonlocal potentials.
J. Chem. Phys. 52, pp. 6211–6217.
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7: Bibliography O
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Studies on the Painlevé equations. I. Sixth Painlevé equation
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Ann. Mat. Pura Appl. (4) 146, pp. 337–381.
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A further method for the evaluation of zeros of Bessel functions and some new asymptotic expansions for zeros of functions of large order.
Proc. Cambridge Philos. Soc. 47, pp. 699–712.
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Some new asymptotic expansions for Bessel functions of large orders.
Proc. Cambridge Philos. Soc. 48 (3), pp. 414–427.
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Uniform asymptotic expansions for Weber parabolic cylinder functions of large orders.
J. Res. Nat. Bur. Standards Sect. B 63B, pp. 131–169.
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Iterative Solution of Nonlinear Equations in Several Variables.
Academic Press, New York.
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8: Bibliography W
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The Algebraic Eigenvalue Problem.
Monographs on Numerical Analysis. Oxford Science Publications, The Clarendon Press, Oxford University Press, Oxford.
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Computation with Recurrence Relations.
Pitman, Boston, MA.
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On the asymptotic behavior of the Fourier coefficients of Mathieu functions.
J. Res. Nat. Inst. Standards Tech. 113 (1), pp. 11–15.
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Quadrature formulas for oscillatory integral transforms.
Numer. Math. 39 (3), pp. 351–360.
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Asymptotic Approximations of Integrals.
Academic Press Inc., Boston-New York.
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9: Bibliography C
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A quadrature formula for the Hankel transform.
Numer. Algorithms 9 (2), pp. 343–354.
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An algorithm for the Fourier-Bessel transform.
Comput. Phys. Comm. 23 (4), pp. 343–353.
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Permutation symmetry for theta functions.
J. Math. Anal. Appl. 378 (1), pp. 42–48.
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Optimized fast Hankel transform filters.
Geophysical Prospecting 38 (5), pp. 545–568.
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Computation of Hankel transforms.
SIAM Rev. 14 (2), pp. 278–285.
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10: Bibliography T
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Asymptotic estimates of Stirling numbers.
Stud. Appl. Math. 89 (3), pp. 233–243.
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Asymptotic Methods for Integrals.
Series in Analysis, Vol. 6, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ.
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High Speed Numerical Integration of Fermi Dirac Integrals.
Master’s Thesis, Naval Postgraduate School, Monterey, CA.
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The Theory of Functions.
2nd edition, Oxford University Press, Oxford.
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Numerical Linear Algebra.
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
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