Racah%20polynomials
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11: Wolter Groenevelt
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►Groenevelt’s research interests is in special functions and orthogonal polynomials and their relations with representation theory and interacting particle systems.
►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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12: Bibliography C
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A note on Euler numbers and polynomials.
Nagoya Math. J. 7, pp. 35–43.
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Asymptotic estimates for generalized Stirling numbers.
Analysis (Munich) 20 (1), pp. 1–13.
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Asymptotics of Racah coefficients and polynomials.
J. Phys. A 32 (3), pp. 537–553.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
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13: 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.
14: 20 Theta Functions
Chapter 20 Theta Functions
…15: 18.5 Explicit Representations
16: 16.4 Argument Unity
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►The characterizing properties (18.22.2), (18.22.10), (18.22.19), (18.22.20), and (18.26.14) of the Hahn and Wilson class polynomials are examples of the contiguous relations mentioned in the previous three paragraphs.
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►One example of such a three-term relation is the recurrence relation (18.26.16) for Racah polynomials.
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17: 24.2 Definitions and Generating Functions
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§24.2(i) Bernoulli Numbers and Polynomials
… ►§24.2(ii) Euler Numbers and Polynomials
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18: 1.11 Zeros of Polynomials
§1.11 Zeros of Polynomials
… ►Horner’s Scheme
… ►§1.11(ii) Elementary Properties
… ►The discriminant of is defined by … ►§1.11(v) Stable Polynomials
…19: 3.8 Nonlinear Equations
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§3.8(iv) Zeros of Polynomials
►The polynomial … ►Example. Wilkinson’s Polynomial
… ►Consider and . We have and . …20: 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 associated Wilson polynomials.
Canad. J. Math. 42 (4), pp. 659–695.
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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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Classical and Quantum Orthogonal Polynomials in One Variable.
Encyclopedia of Mathematics and its Applications, Vol. 98, Cambridge University Press, Cambridge.
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