orthogonal polynomials with Freud weights

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1: 18.32 OP’s with Respect to Freud Weights

§18.32 OP’s with Respect to Freud Weights

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2: Bibliography K

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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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BibTeX

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3: 18.38 Mathematical Applications

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Quadrature

… ►If the nodes in a quadrature formula with a positive weight function are chosen to be the zeros of the $n$th degree OP with the same weight function, and the interval of orthogonality is the same as the integration range, then the weights in the quadrature formula can be chosen in such a way that the formula is exact for all polynomials of degree not exceeding $2n-1$. … ►Hermite polynomials (and their Freud-weight analogs (§18.32)) play an important role in random matrix theory. … ►

Riemann–Hilbert Problems

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Group Representations

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4: Bibliography F

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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. II. J. Math. Anal. Appl. 7 (3), pp. 440–451.

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External Links:

Document, MathReview (L. J. Slater), ZentralBlatt

Referenced by:

§16.11(iii).

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BibTeX

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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. J. Math. Anal. Appl. 6 (3), pp. 394–403.

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External Links:

Document, MathReview (L. J. Slater), ZentralBlatt

Referenced by:

§16.11(iii).

Encodings:

BibTeX

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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. III. J. Math. Anal. Appl. 12 (3), pp. 593–601.

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External Links:

Document, MathReview (M. J. O. Strutt), ZentralBlatt

Referenced by:

§16.11(iii).

Encodings:

BibTeX

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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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External Links:

ISSN 0001-5954, Document, Link, MathReview (A. K. Varma)

Referenced by:

§18.32.

Encodings:

BibTeX

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On the coefficients in the recursion formulae of orthogonal polynomials. Proc. Roy. Irish Acad. Sect. A 76 (1), pp. 1–6.

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External Links:

MathReview (A. G. Law), ZentralBlatt

Referenced by:

§18.32, §32.15.

Encodings:

BibTeX

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5: 18.39 Applications in the Physical Sciences

… ►and eigenvalues $n+3$, with $n$ as above, with $w(x)$ the weight function of (18.36.10), and ${\widehat{H}}_{n+3}\left(x\right)$ a type III Hermite EOP defined by (18.36.8) and (18.36.9). … ►

§18.39(iii) Non Classical Weight Functions of Utility in DVR Method in the Physical Sciences

… ►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. … ►These cases correspond to the two distinct orthogonality conditions of (18.35.6) and (18.35.6_3). … ►For interpretations of zeros of classical OP’s as equilibrium positions of charges in electrostatic problems (assuming logarithmic interaction), see Ismail (2000a, b).