orthogonal%20polynomials
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1: Wolter Groenevelt
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►As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials.
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2: Bibliography G
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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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3: Bibliography K
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Orthogonal Polynomials on -spheres: Gegenbauer, Jacobi and Heun.
In Topics in Polynomials of One and Several Variables and their
Applications,
pp. 299–322.
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Orthogonal polynomials and computer algebra.
In Recent developments in complex analysis and computer algebra
(Newark, DE, 1997), R. P. Gilbert, J. Kajiwara, and Y. S. Xu (Eds.),
Int. Soc. Anal. Appl. Comput., Vol. 4, Dordrecht, pp. 205–234.
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Two-variable Analogues of the Classical Orthogonal Polynomials.
In Theory and Application of Special Functions, R. A. Askey (Ed.),
pp. 435–495.
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Lowering and Raising Operators for Some Special Orthogonal Polynomials.
In Jack, Hall-Littlewood and Macdonald Polynomials,
Contemp. Math., Vol. 417, pp. 227–238.
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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: 18.5 Explicit Representations
§18.5 Explicit Representations
… ►§18.5(iii) Finite Power Series, the Hypergeometric Function, and Generalized Hypergeometric Functions
… ►However, in these circumstances the orthogonality property (18.2.1) disappears. … … ►5: Bibliography I
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The real roots of Bernoulli polynomials.
Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
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On polynomials orthogonal with respect to certain Sobolev inner products.
J. Approx. Theory 65 (2), pp. 151–175.
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Two families of orthogonal polynomials related to Jacobi polynomials.
Rocky Mountain J. Math. 21 (1), pp. 359–375.
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An electrostatics model for zeros of general orthogonal polynomials.
Pacific J. Math. 193 (2), pp. 355–369.
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Classical and Quantum Orthogonal Polynomials in One Variable.
Encyclopedia of Mathematics and its Applications, Vol. 98, Cambridge University Press, Cambridge.
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6: Bibliography V
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Expansions in products of Heine-Stieltjes polynomials.
Constr. Approx. 15 (4), pp. 467–480.
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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation.
Constr. Approx. 20 (1), pp. 39–54.
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Approximation of eigenvalues of some differential equations by zeros of orthogonal polynomials.
J. Comput. Appl. Math. 213 (2), pp. 488–500.
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7: Software Index
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18 Orthogonal Polynomials | |||||||||||||||||||||||||
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20 Theta Functions | |||||||||||||||||||||||||
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24 Bernoulli and Euler Polynomials | |||||||||||||||||||||||||
24.21(ii) , , , | ✓ | ✓ | ✓ | ✓ | a | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | Derive, MuPAD | ||||||||||||
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8: Bibliography D
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Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach.
Courant Lecture Notes in Mathematics, Vol. 3, New York University Courant Institute of Mathematical
Sciences, New York.
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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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Sharp bounds for the extreme zeros of classical orthogonal polynomials.
J. Approx. Theory 162 (10), pp. 1793–1804.
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Orthogonal polynomials and the construction of piecewise polynomial smooth wavelets.
SIAM J. Math. Anal. 30 (5), pp. 1029–1056.
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Inequalities for extreme zeros of some classical orthogonal and -orthogonal polynomials.
Math. Model. Nat. Phenom. 8 (1), pp. 48–59.
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9: William P. Reinhardt
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►Reinhardt is a theoretical chemist and atomic physicist, who has always been interested in orthogonal polynomials and in the analyticity properties of the functions of mathematical physics.
…Older work on the scattering theory of the atomic Coulomb problem led to the discovery of new classes of orthogonal polynomials relating to the spectral theory of Schrödinger operators, and new uses of old ones: this work was strongly motivated by his original ownership of a 1964 hard copy printing of the original AMS 55 NBS Handbook of Mathematical Functions.
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►In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.
10: Bibliography B
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Orthogonal Polynomials in Coding Theory and Algebraic Combinatorics.
In Orthogonal Polynomials (Columbus, OH, 1989),
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Vol. 294, pp. 25–53.
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The Bounds for the Error Term of an Asymptotic Approximation of Jacobi Polynomials.
In Orthogonal Polynomials and Their Applications (Segovia, 1986),
Lecture Notes in Math., Vol. 1329, pp. 203–221.
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Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model.
Ann. of Math. (2) 150 (1), pp. 185–266.
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A uniform asymptotic formula for orthogonal polynomials associated with
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J. Approx. Theory 98, pp. 146–166.
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Padé-type Approximation and General Orthogonal Polynomials.
International Series of Numerical Mathematics, Vol. 50, Birkhäuser Verlag, Basel.
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