discrete weights

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11: 18.2 General Orthogonal Polynomials

… ►For OP’s $\{p_n(x)\}$ on $ℝ$ with respect to an even weight function $w(x)$ we have … ►Under further conditions on the weight function there is an equiconvergence theorem, see Szegő (1975, Theorem 13.1.2). … ►In further generalizations of the class $𝒮$ discrete mass points $x_k$ outside $[-1,1]$ are allowed. … ►

Monotonic Weight Functions

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12: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ► The analogous orthonormality is … ►These sets may be discrete, continuous, or a combination of both, as discussed in the following three subsections. … ►

§1.18(v) Point Spectra and Eigenfunction Expansions

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13: Bibliography G

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A new application of the discrete Laguerre polynomials in the numerical evaluation of the Hankel transform of a strongly decreasing even function. J. Comput. Phys. 42 (2), pp. 277–287.

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External Links:

Document, ZentralBlatt

Referenced by:

§10.74(vii).

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Stable computation of high order Gauss quadrature rules using discretization for measures in radiation transfer. J. Quant. Spectrosc. Radiat. Transfer 68 (2), pp. 213–223.

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Referenced by:

§18.39(iii).

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The GAP Group, Centre for Interdisciplinary Research in Computational Algebra, University of St. Andrews, United Kingdom.

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Notes:

Groups, Algorithms, Programming: A system for computational discrete algebra with emphasis on computational group theory.

External Links:

GAP

Referenced by:

2nd item.

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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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External Links:

ISSN 0008-414X, MathReview (Mourad E. H. Ismail), ZentralBlatt

Referenced by:

§18.33(v).

Encodings:

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14: 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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External Links:

ISSN 0021-9045, Document, Link, MathReview (Walter Van Assche)

Referenced by:

§18.32.

Encodings:

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Orthogonal polynomials with weight function ${(1-x)}^{\alpha }{(1+x)}^{\beta }+M\delta (x+1)+N\delta (x-1)$ . Canad. Math. Bull. 27 (2), pp. 205–214.

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External Links:

ISSN 0008-4395, MathReview (Wolfgang Hahn), ZentralBlatt

Referenced by:

§18.36(i), §18.36(i).

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Jacobi polynomials, Bernstein-type inequalities and dispersion estimates for the discrete Laguerre operator. Adv. Math. 333, pp. 796–821.

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External Links:

ISSN 0001-8708, Document, Link, MathReview (Martin Axel Hallnäs)

Referenced by:

§18.14(i).

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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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External Links:

ISSN 1073-7928, Document, MathReview (Heinrich Begehr), ZentralBlatt

Referenced by:

§18.32.

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