Van Vleck theorem
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11—20 of 157 matching pages
11: 10.74 Methods of Computation
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►To ensure that no zeros are overlooked, standard tools are the phase principle and Rouché’s theorem; see §1.10(iv).
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►For infinite integrals involving products of Bessel functions of the first kind, see Linz and Kropp (1973), Gabutti (1980), Ikonomou et al. (1995), Lucas (1995), and Van Deun and Cools (2008).
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12: Bibliography K
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Auxiliary table for the incomplete elliptic integrals.
J. Math. Physics 27, pp. 11–36.
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Orthonormal polynomials with generalized Freud-type weights.
J. Approx. Theory 121 (1), pp. 13–53.
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A general addition theorem for spheroidal wave functions.
SIAM J. Math. Anal. 4 (1), pp. 149–160.
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A Fortran computer program for calculating the prolate and oblate angle functions of the first kind and their first and second derivatives.
NRL Report No. 7161
Naval Res. Lab. Washingtion, D.C..
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A new proof of a Paley-Wiener type theorem for the Jacobi transform.
Ark. Mat. 13, pp. 145–159.
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13: 34.7 Basic Properties: Symbol
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►For generating functions for the symbol see Biedenharn and van Dam (1965, p. 258, eq. (4.37)).
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►It constitutes an addition theorem for the symbol.
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14: 30.18 Software
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►See also King et al. (1970), King and Van Buren (1970), Van Buren et al. (1970), and Van Buren et al. (1972).
15: 25.10 Zeros
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►Also, for , a property first established in Hadamard (1896) and de la Vallée Poussin (1896a, b) in the proof of the prime number theorem (25.16.3).
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►Calculations based on the Riemann–Siegel formula reveal that the first ten billion zeros of in the critical strip are on the critical line (van de Lune et al. (1986)).
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16: Bibliography G
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WKB and turning point theory for second-order difference equations.
In Spectral Methods for Operators of Mathematical Physics,
Oper. Theory Adv. Appl., Vol. 154, pp. 101–138.
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A theorem on the numerators of the Bernoulli numbers.
Amer. Math. Monthly 97 (2), pp. 136–138.
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Matrix Computations.
3rd edition, Johns Hopkins University Press, Baltimore, MD.
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Table of
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Quart. J. Mech. Appl. Math. 1 (1), pp. 319–326.
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Inductance Calculations.
Van Nostrand, New York.
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17: 5.21 Methods of Computation
18: Tom H. Koornwinder
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19: Bibliography B
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Quantum mechanics of one- and two-electron atoms.
Springer-Verlag, Berlin.
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Quantum Theory of Angular Momentum. A Collection of Reprints and Original Papers.
Academic Press, New York.
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Uniform asymptotic expansions of integrals with stationary point near algebraic singularity.
Comm. Pure Appl. Math. 19, pp. 353–370.
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Bessel functions and modular relations of higher type and hyperbolic differential equations.
Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (Tome Supplementaire), pp. 12–20.
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Faster Primality Testing.
In Advances in Cryptology—EUROCRYPT ’89 Proceedings, J.-J. Quisquater and J. Vandewalle (Eds.),
Lecture Notes in Computer Science, Vol. 434, New York, pp. 652–656.
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