associated orthogonal polynomials

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1: 18.30 Associated OP’s

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§18.30(ii) Associated Legendre Polynomials

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§18.30(iii) Associated Laguerre Polynomials

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§18.30(iv) Associated Hermite Polynomials

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§18.30(vii) Corecursive and Associated Monic Orthogonal Polynomials

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2: 18.37 Classical OP’s in Two or More Variables

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§18.37(iii) OP’s Associated with Root Systems

►Orthogonal polynomials associated with root systems are certain systems of trigonometric polynomials in several variables, symmetric under a certain finite group (Weyl group), and orthogonal on a torus. …

3: 18.2 General Orthogonal Polynomials

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§18.2(x) Orthogonal Polynomials and Continued Fractions

… ►Define the first associated monic orthogonal polynomials $p_n^{(1)}(x)$ as monic OP’s satisfying … ► …

4: Bibliography M

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Orthogonal polynomials associated with root systems. Sém. Lothar. Combin. 45, pp. Art. B45a, 40 pp. (electronic).

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External Links:

ISSN 1286-4889, FullText, MathReview, ZentralBlatt

Referenced by:

§18.37(iii).

Encodings:

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The supports of measures associated with orthogonal polynomials and the spectra of the related selfadjoint operators. Rocky Mountain J. Math. 21 (1), pp. 501–527.

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External Links:

ISSN 0035-7596, Document, Link, MathReview (T. S. Chihara)

Referenced by:

§18.2(xi).

Encodings:

BibTeX

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5: Bibliography R

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The Associated Classical Orthogonal Polynomials. In Special Functions 2000: Current Perspective and Future Directions (Tempe, AZ), NATO Sci. Ser. II Math. Phys. Chem., Vol. 30, pp. 255–279.

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External Links:

MathReview (Wadim Zudilin), ZentralBlatt

Referenced by:

§18.30(viii).

Encodings:

BibTeX

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6: Bibliography B

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On the Associated Legendre Polynomials. In Orthogonal Expansions and their Continuous Analogues (Proc. Conf., Edwardsville, Ill., 1967), pp. 43–50.

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External Links:

MathReview (B. R. Bhonsle), ZentralBlatt

Referenced by:

§18.30.

Encodings:

BibTeX

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A uniform asymptotic formula for orthogonal polynomials associated with $\exp (-x^4)$ . J. Approx. Theory 98, pp. 146–166.

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External Links:

ISSN 0021-9045, Document, MathReview (V. L. Deshpande), ZentralBlatt

Referenced by:

§18.32.

Encodings:

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7: 18 Orthogonal Polynomials

Chapter 18 Orthogonal Polynomials

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8: 16.18 Special Cases

… ►As a corollary, special cases of the ${}_1{}^{}F_1^{}$ and ${}_2{}^{}F_1^{}$ functions, including Airy functions, Bessel functions, parabolic cylinder functions, Ferrers functions, associated Legendre functions, and many orthogonal polynomials, are all special cases of the Meijer $G$-function. …

9: 34 3j, 6j, 9j Symbols

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10: 2.9 Difference Equations

… ►These methods are particularly useful when the weight function associated with the orthogonal polynomials is not unique or not even known; see, e. …