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8 matching pages
1: Bibliography F
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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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2: 18.40 Methods of Computation
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A numerical approach to the recursion coefficients and quadrature abscissas and weights
… ►These quadrature weights and abscissas will then allow construction of a convergent sequence of approximations to , as will be considered in the following paragraphs. … ►The quadrature abscissas and weights then follow from the discussion of §3.5(vi). … ►Results of low ( to decimal digits) precision for are easily obtained for to . … ►The quadrature points and weights can be put to a more direct and efficient use. …3: Bibliography K
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Orthonormal polynomials with generalized Freud-type weights.
J. Approx. Theory 121 (1), pp. 13–53.
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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Strong asymptotics of polynomials orthogonal with respect to Freud weights.
Internat. Math. Res. Notices 1999 (6), pp. 299–333.
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4: 18.39 Applications in the Physical Sciences
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§18.39(iii) Non Classical Weight Functions of Utility in DVR Method in the Physical Sciences
… ►For many applications the natural weight functions are non-classical, and thus the OP’s and the determination of the Gaussian quadrature points and weights represent a computational challenge. Table 18.39.1 lists typical non-classical weight functions, many related to the non-classical Freud weights of §18.32, and §32.15, all of which require numerical computation of the recursion coefficients (i. …Shizgal (2015, Chapter 2), contains a broad-ranged discussion of methods and applications for these, and other, non-classical weight functions. … ►Graphs of the weight functions of (18.39.50) are shown in Figure 18.39.2. …5: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics.
Comput. Phys. Comm. 150 (1), pp. 1–20.
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Szegő Type Asymptotics for the Reproducing Kernel in Spaces of Full-Plane Weighted Polynomials.
Comm. Math. Phys. 398 (3), pp. 1291–1348.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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6: Bibliography R
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On the definition and properties of generalized - symbols.
J. Math. Phys. 20 (12), pp. 2398–2415.
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Erratum to:Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging.
Computing in Science and Engineering 23 (4), pp. 91.
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Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging.
Computing in Science and Engineering 23 (3), pp. 56–64.
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7: Bibliography G
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Orthogonality of certain functions with respect to complex valued weights.
Canad. J. Math. 33 (5), pp. 1261–1270.
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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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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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8: Bibliography D
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Strong asymptotics of orthogonal polynomials with respect to exponential weights.
Comm. Pure Appl. Math. 52 (12), pp. 1491–1552.
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Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory.
Comm. Pure Appl. Math. 52 (11), pp. 1335–1425.
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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Functions with given moments and weight functions for orthogonal polynomials.
Rocky Mountain J. Math. 23, pp. 87–104.
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