approximation theory

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1: Mourad E. H. Ismail

… ►Ismail has published numerous papers on special functions, orthogonal polynomials, approximation theory, combinatorics, asymptotics, and related topics. … ►Ismail serves on several editorial boards including the Cambridge University Press book series Encyclopedia of Mathematics and its Applications, and on the editorial boards of 9 journals including Proceedings of the American Mathematical Society (Integrable Systems and Special Functions Editor); Constructive Approximation; Journal of Approximation Theory; and Integral Transforms and Special Functions. …

2: Annie A. M. Cuyt

… ►Her main research interest is in the area of numerical approximation theory and its applications to a diversity of problems in scientific computing. …

3: 18.38 Mathematical Applications

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§18.38(i) Classical OP’s: Numerical Analysis

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Approximation Theory

… ►For these results and applications in approximation theory see §3.11(ii) and Mason and Handscomb (2003, Chapter 3), Cheney (1982, p. 108), and Rivlin (1969, p. 31). …

4: Bibliography W

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The method of Darboux. J. Approximation Theory 10 (2), pp. 159–171.

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External Links:

Document, MathReview (M. E. Noble), ZentralBlatt

Referenced by:

§2.10(iv).

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On uniform asymptotic expansion of definite integrals. J. Approximation Theory 7 (1), pp. 76–86.

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External Links:

Document, MathReview (L. Berg), ZentralBlatt

Referenced by:

§8.11(v).

Encodings:

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5: 12.16 Mathematical Applications

… ►PCFs are used as basic approximating functions in the theory of contour integrals with a coalescing saddle point and an algebraic singularity, and in the theory of differential equations with two coalescing turning points; see §§2.4(vi) and 2.8(vi). …

6: Bibliography T

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Numerical and asymptotic aspects of parabolic cylinder functions. J. Comput. Appl. Math. 121 (1-2), pp. 221–246.

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Notes:

Numerical analysis in the 20th century, Vol. I, Approximation theory

External Links:

ISSN 0377-0427, Document, MathReview (José Luis López), ZentralBlatt

Referenced by:

§12.10(vii), §12.10(vi), §12.10(vi), §12.18.

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7: Bibliography C

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Introduction to Approximation Theory. 2nd edition, Chelsea Publishing Co., New York.

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Notes:

Reprinted by AMS Chelsea Publishing, Providence, RI, 1998

External Links:

ISBN 0-8218-1374-9, MathReview, ZentralBlatt

Referenced by:

§18.38(i).

Encodings:

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Further formulas for calculating approximate values of the zeros of certain combinations of Bessel functions. IEEE Trans. Microwave Theory Tech. 11 (6), pp. 546–547.

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External Links:

ISSN 0018-9480, FullText

Referenced by:

§10.21(x).

Encodings:

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8: Bibliography M

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Approximation of Functions: Theory and Numerical Methods. Springer Tracts in Natural Philosophy, Vol. 13, Springer-Verlag, New York.

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Notes:

Expanded translation from the German edition. Translated by Larry L. Schumaker

External Links:

MathReview, ZentralBlatt

Referenced by:

§3.11(i), §3.11(iii).

Encodings:

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Exceptional orthogonal polynomials.

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Notes:

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

Referenced by:

§18.36(vi), §18.38(iii).

Encodings:

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9: 3.11 Approximation Techniques

… ►For the theory of minimax approximations see Meinardus (1967). … ►The theory of polynomial minimax approximation given in §3.11(i) can be extended to the case when $p_n(x)$ is replaced by a rational function $R_{k,\mathrm{\ell }}(x)$. …

10: Bibliography B

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Uniform approximation: A new concept in wave theory. Science Progress (Oxford) 57, pp. 43–64.

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Referenced by:

§36.14(i), §9.16.

Encodings:

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