quadratic Jacobi symbol
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6 matching pages
1: 27.9 Quadratic Characters
2: Bibliography
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Integral representations for Jacobi polynomials and some applications.
J. Math. Anal. Appl. 26 (2), pp. 411–437.
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Positive Jacobi polynomial sums. II.
Amer. J. Math. 98 (3), pp. 709–737.
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An integral for Jacobi polynomials.
Simon Stevin 46, pp. 165–169.
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Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials.
Mem. Amer. Math. Soc. 54 (319), pp. iv+55.
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Quadratic differentials and asymptotics of Laguerre polynomials with varying complex parameters.
J. Math. Anal. Appl. 416 (1), pp. 52–80.
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3: 18.7 Interrelations and Limit Relations
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Ultraspherical and Jacobi
… ►Chebyshev, Ultraspherical, and Jacobi
… ►§18.7(ii) Quadratic Transformations
… ►Equations (18.7.13)–(18.7.20) are special cases of (18.2.22)–(18.2.23). … ►Jacobi Hermite
…4: 18.19 Hahn Class: Definitions
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►The Askey scheme extends the three families of classical OP’s (Jacobi, Laguerre and Hermite) with eight further families of OP’s for which the role of the differentiation operator in the case of the classical OP’s is played by a suitable difference operator.
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Wilson class (or quadratic lattice class). These are OP’s ( of degree in , quadratic in ) where the role of the differentiation operator is played by or or . The Wilson class consists of two discrete and two continuous families.
18.19.5
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5: 18.33 Polynomials Orthogonal on the Unit Circle
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►After a quadratic transformation (18.2.23) this would express OP’s on with an even orthogonality measure in terms of the .
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18.33.13
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►Askey (1982a) and Sri Ranga (2010) give more general results leading to what seem to be the right analogues of Jacobi polynomials on the unit circle.
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18.33.15
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18.33.16
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6: 18.27 -Hahn Class
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►The
-hypergeometric OP’s comprise the -Hahn class (or -linear lattice class) OP’s and the Askey–Wilson class (or -quadratic lattice class) OP’s (§18.28).
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