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11: Bibliography C

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Work Group of Computational Mathematics, University of Kassel, Germany.

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Computer Algebra and Orthogonal Polynomials: a Web service using Maple for online generation of formulas and graphs of orthogonal polynomials belonging to the Askey scheme. For further information see Swarttouw (1997) and Koepf (1999).

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CAOP

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1st item.

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Asymptotics of the largest zeros of some orthogonal polynomials. J. Phys. A 31 (25), pp. 5525–5544.

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ISSN 0305-4470, Document, MathReview (Tim H. Baker), ZentralBlatt

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§18.26(v), §18.29.

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An Introduction to Orthogonal Polynomials. Mathematics and its Applications, Vol. 13, Gordon and Breach Science Publishers, New York.

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ISBN 0-677-04150-0, MathReview (A. G. Law), ZentralBlatt

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§1.16(ix), (18.2.33), (18.2.36), (18.2.38), §18.2(v), §18.2(iii), §18.2(iv), §18.2(vii), §18.2(x), §18.20(i), (18.30.25), §18.30(ii), §18.30, §18.40(ii), Ch.18.

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Extremal measures for a system of orthogonal polynomials. Constr. Approx. 9, pp. 111–119.

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ISSN 0176-4276, Document, MathReview (Mizan Rahman), ZentralBlatt

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§18.28(iv).

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Basic hypergeometric functions and orthogonal Laurent polynomials. Proc. Amer. Math. Soc. 140 (6), pp. 2075–2089.

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ISSN 0002-9939, Link, MathReview (Roelof Koekoek), ZentralBlatt

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§18.33(iv).

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12: Bibliography P

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Zonal Polynomials of Order $1$ Through $12$ . In Selected Tables in Mathematical Statistics, H. L. Harter and D. B. Owen (Eds.), Vol. 2, pp. 199–388.

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MathReview

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§35.11.

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Orthogonal polynomials and some $q$-beta integrals of Ramanujan. J. Math. Anal. Appl. 112 (2), pp. 517–540.

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ISSN 0022-247X, Document, MathReview (Mourad E. H. Ismail), ZentralBlatt

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§18.33(iv), §18.33(v).

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A new basis for the representation of the rotation group. Lamé and Heun polynomials. J. Mathematical Phys. 14 (8), pp. 1130–1139.

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Document, ZentralBlatt

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§29.18(iv).

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Automatic computation of Bessel function integrals. Comput. Phys. Comm. 25 (3), pp. 289–295.

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Double-precision Fortran, maximum accuracy 20S.

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ISSN 0010-4655, Document, Code

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6th item.

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Chebyshev polynomial expansions of the Riemann zeta function. Math. Comp. 26 (120), pp. G1–G5.

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ISSN 0025-5718, FullText, MathReview

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2nd item, 3rd item.

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13: Bibliography M

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Symmetric Functions and Orthogonal Polynomials. University Lecture Series, Vol. 12, American Mathematical Society, Providence, RI.

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ISBN 0-8218-0770-6, MathReview (Angèle M. Hamel), ZentralBlatt

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§17.14.

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

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ISSN 1286-4889, FullText, MathReview, ZentralBlatt

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§18.37(iii).

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Affine Hecke Algebras and Orthogonal Polynomials. Cambridge Tracts in Mathematics, Vol. 157, Cambridge University Press, Cambridge.

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ISBN 0-521-82472-9, MathReview (Eric M. Opdam), ZentralBlatt

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§18.37(iii).

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Exceptional orthogonal polynomials.

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Lecture at ICMAT School on Orthogonal Polynomials in Approximation Theory and Mathematical Physics, available at https://www.icmat.es/RT/optrim/school/lectures/Milson/icmat17.pdf

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§18.36(vi), §18.38(iii).

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The $q$-analogue of the Laguerre polynomials. J. Math. Anal. Appl. 81 (1), pp. 20–47.

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ISSN 0022-247X, Document, MathReview (R. A. Askey), ZentralBlatt

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§18.27(v).

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14: Bibliography R

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A non-negative representation of the linearization coefficients of the product of Jacobi polynomials. Canad. J. Math. 33 (4), pp. 915–928.

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ISSN 0008-414X, Document, Link, MathReview (R. A. Askey), ZentralBlatt

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§18.18(v).

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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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MathReview (Wadim Zudilin), ZentralBlatt

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§18.30(viii).

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On the definition and properties of generalized $6$-$j$ symbols. J. Math. Phys. 20 (12), pp. 2398–2415.

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ISSN 0022-2488, Document, MathReview (S. Saran), ZentralBlatt

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§16.4(iii), §16.4(iii).

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Erratum to:Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging. Computing in Science and Engineering 23 (4), pp. 91.

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ISSN 1521-9615, Document, Link

Referenced by:

§18.39(iv), §18.40(ii).

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Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging. Computing in Science and Engineering 23 (3), pp. 56–64.

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ISSN 1521-9615, Document, Link

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§18.39(iv), §18.40(ii).

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15: Bibliography N

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On an integral transform involving a class of Mathieu functions. SIAM J. Math. Anal. 20 (6), pp. 1500–1513.

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ISSN 0036-1410, Document, MathReview (K. C. Gupta), ZentralBlatt

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§28.26(ii).

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Reduction and evaluation of elliptic integrals. Math. Comp. 20 (94), pp. 223–231.

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FullText, MathReview (I. A. Stegun), ZentralBlatt

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§19.37(iv).

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Orthogonal polynomials. Mem. Amer. Math. Soc. 18 (213), pp. v+185 pp..

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ISSN 0065-9266, Document, Link, MathReview (T. S. Chihara)

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§18.2(xi), §18.2(xi).

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Géza Freud, orthogonal polynomials and Christoffel functions. A case study. J. Approx. Theory 48 (1), pp. 3–167.

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ISSN 0021-9045, Document, MathReview (T. S. Chihara), ZentralBlatt

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§18.32.

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Askey-Wilson polynomials: an affine Hecke algebra approach. In Laredo Lectures on Orthogonal Polynomials and Special Functions, Adv. Theory Spec. Funct. Orthogonal Polynomials, pp. 111–144.

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MathReview (V. L. Deshpande), ZentralBlatt

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§18.38(iii).

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16: Bibliography L

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Algorithm 917: complex double-precision evaluation of the Wright $\omega$ function. ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.

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ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt

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§4.13, 2nd item, §4.48(iv).

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Orthogonal polynomials, duality and association schemes. SIAM J. Math. Anal. 13 (4), pp. 656–663.

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ISSN 0036-1410, Document, MathReview (C. L. Parihar), ZentralBlatt

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§18.28(viii), §18.28(xi), §18.38(iii).

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Orthogonal Polynomials for Exponential Weights. CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 4, Springer-Verlag, New York.

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ISBN 0-387-98941-2, MathReview (Walter Van Assche), ZentralBlatt

Referenced by:

§18.32.

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Orthogonal polynomials for exponential weights $x^{2\rho }{e}^{-2Q(x)}$ on $[0,d)$ . J. Approx. Theory 134 (2), pp. 199–256.

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ISSN 0021-9045, Document, Link, MathReview (Leonid B. Golinskiĭ)

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§18.32.

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Approximation of orthogonal polynomials in terms of Hermite polynomials. Methods Appl. Anal. 6 (2), pp. 131–146.

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ISSN 1073-2772, Pdf, MathReview, ZentralBlatt

Referenced by:

§18.15(vi), §18.16(vi).

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17: 3.8 Nonlinear Equations

… ►For the computation of zeros of orthogonal polynomials as eigenvalues of finite tridiagonal matrices (§3.5(vi)), see Gil et al. (2007a, pp. 205–207). … ►The polynomial … ►

Example. Wilkinson’s Polynomial

… ►Consider $x=20$ and $j=19$. We have $p^{\prime }(20)=19!$ and $a_{19}=1+2+\mathrm{\cdots }+20=210$. …

18: 18.39 Applications in the Physical Sciences

… ►Kuijlaars and Milson (2015, §1) refer to these, in this case complex zeros, as exceptional, as opposed to regular, zeros of the EOP’s, these latter belonging to the (real) orthogonality integration range. … ►Derivations of (18.39.42) appear in Bethe and Salpeter (1957, pp. 12–20), and Pauling and Wilson (1985, Chapter V and Appendix VII), where the derivations are based on (18.39.36), and is also the notation of Piela (2014, §4.7), typifying the common use of the associated Coulomb–Laguerre polynomials in theoretical quantum chemistry. … ►

The Coulomb–Pollaczek Polynomials

… ►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).