classical%20orthogonal%20polynomials
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11—15 of 15 matching pages
11: Bibliography G
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Positive sums of the classical orthogonal polynomials.
SIAM J. Math. Anal. 8 (3), pp. 423–447.
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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules.
ACM Trans. Math. Software 20 (1), pp. 21–62.
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Orthogonal Polynomials: Applications and Computation.
In Acta Numerica, 1996, A. Iserles (Ed.),
Acta Numerica, Vol. 5, pp. 45–119.
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Orthogonal Polynomials: Computation and Approximation.
Numerical Mathematics and Scientific Computation, Oxford University Press, New York.
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Variable-precision recurrence coefficients for nonstandard orthogonal polynomials.
Numer. Algorithms 52 (3), pp. 409–418.
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12: Bibliography L
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Orthogonal polynomials, duality and association schemes.
SIAM J. Math. Anal. 13 (4), pp. 656–663.
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Orthogonal Polynomials for Exponential Weights.
CMS Books in Mathematics/Ouvrages de Mathématiques de la
SMC, 4, Springer-Verlag, New York.
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Orthogonal polynomials for exponential weights on
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J. Approx. Theory 134 (2), pp. 199–256.
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Kinetic Theory: Classical, Quantum, and Relativistic Descriptions.
third edition, Springer, New York.
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Approximation of orthogonal polynomials in terms of Hermite polynomials.
Methods Appl. Anal. 6 (2), pp. 131–146.
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13: Bibliography W
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Asymptotics of orthogonal polynomials via recurrence relations.
Anal. Appl. (Singap.) 10 (2), pp. 215–235.
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The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
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Elliptic Functions According to Eisenstein and Kronecker.
Classics in Mathematics, Springer-Verlag, Berlin.
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Hypergeometric Series, Recurrence Relations and Some New Orthogonal Polynomials.
Ph.D. Thesis, University of Wisconsin, Madison, WI.
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Some hypergeometric orthogonal polynomials.
SIAM J. Math. Anal. 11 (4), pp. 690–701.
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14: Bibliography C
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Work Group of Computational Mathematics, University of Kassel, Germany.
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Asymptotics of the largest zeros of some orthogonal polynomials.
J. Phys. A 31 (25), pp. 5525–5544.
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An Introduction to Orthogonal Polynomials.
Mathematics and its Applications, Vol. 13, Gordon and Breach Science Publishers, New York.
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Extremal measures for a system of orthogonal polynomials.
Constr. Approx. 9, pp. 111–119.
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Basic hypergeometric functions and orthogonal Laurent polynomials.
Proc. Amer. Math. Soc. 140 (6), pp. 2075–2089.
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15: 18.39 Applications in the Physical Sciences
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►As in classical dynamics this sum is the total energy of the one particle system.
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►This indicates that the Laguerre polynomials appearing in (18.39.29) are not classical OP’s, and in fact, even though infinite in number for fixed , do not form a complete set.
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►Derivations of (18.39.42) appear in Bethe and Salpeter (1957, pp. 12–20), and Pauling and Wilson (1985, Chapter V and Appendix VII), where the derivations are based on (18.39.36), and is also the notation of Piela (2014, §4.7), typifying the common use of the associated Coulomb–Laguerre polynomials in theoretical quantum chemistry.
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►These cases correspond to the two distinct orthogonality conditions of (18.35.6) and (18.35.6_3).
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►For interpretations of zeros of classical OP’s as equilibrium positions of charges in electrostatic problems (assuming logarithmic interaction), see Ismail (2000a, b).