Chebyshev series

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31: Bibliography F

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Basic Hypergeometric Series and Applications. Mathematical Surveys and Monographs, Vol. 27, American Mathematical Society, Providence, RI.

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Notes:

With a foreword by George E. Andrews

External Links:

ISBN 0-8218-1524-5, MathReview (David M. Bressoud), ZentralBlatt

Referenced by:

§17.1, §17.16, §17.6(ii), Ch.17, Notations F.

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Studies on Divergent Series and Summability & The Asymptotic Developments of Functions Defined by Maclaurin Series. Chelsea Publishing Co., New York.

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Notes:

Reprint with corrections of two books published originally in 1916 and 1936.

External Links:

MathReview

Referenced by:

§2.10(iii).

Encodings:

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Chebyshev Polynomials in Numerical Analysis. Oxford University Press, London.

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Notes:

Reprinted in 1972 with corrections.

External Links:

MathReview (G. N. Lance), ZentralBlatt

Referenced by:

§3.11(ii).

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BibTeX

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Asymptotic expansions of the Lebesgue constants for Jacobi series. Pacific J. Math. 122 (2), pp. 391–415.

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External Links:

ISSN 0030-8730, MathReview (Paolo M. Soardi), ZentralBlatt

Referenced by:

§1.8(i).

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Series expansions of symmetric elliptic integrals. Math. Comp. 81 (278), pp. 957–990.

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External Links:

Document, ZentralBlatt

Referenced by:

§20.7(ii), §20.7(ii).

Encodings:

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32: 18.5 Explicit Representations

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Chebyshev

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Chebyshev

… ►For corresponding formulas for Chebyshev, Legendre, and the Hermite ${\mathrm{𝐻𝑒}}_n$ polynomials apply (18.7.3)–(18.7.6), (18.7.9), and (18.7.11). … ►

Chebyshev

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33: Bibliography B

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Products of generalized hypergeometric series. Proc. London Math. Soc. (2) 28 (2), pp. 242–254.

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External Links:

Document, ZentralBlatt

Referenced by:

§16.12.

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Transformations of generalized hypergeometric series. Proc. London Math. Soc. (2) 29 (2), pp. 495–502.

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External Links:

Document, ZentralBlatt

Referenced by:

§16.6.

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Evaluation of the incomplete gamma function of imaginary argument by Chebyshev polynomials. Math. Comp. 15 (73), pp. 7–11.

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External Links:

FullText, MathReview (J. C. P. Miller), ZentralBlatt

Referenced by:

§8.7.

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Rational Chebyshev approximations for the inverse of the error function. Math. Comp. 30 (136), pp. 827–830.

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External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§7.17(iii), §7.17(iii).

Encodings:

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Rational Chebyshev approximations for the Bickley functions $K{i}_n(x)$ . Math. Comp. 32 (143), pp. 876–886.

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External Links:

ISSN 0025-5718, FullText, MathReview (H. Hochstadt), ZentralBlatt

Referenced by:

§10.76(iii).

Encodings:

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34: 3.5 Quadrature

… ►For the latter $a=-1$, $b=1$, and the nodes $x_k$ are the extrema of the Chebyshev polynomial $T_n\left(x\right)$ (§3.11(ii) and §18.3). … ►

Gauss–Chebyshev Formula

… ► … ►The integral is written as an alternating series of positive and negative subintegrals that are computed individually; see Longman (1956). Convergence acceleration schemes, for example Levin’s transformation (§3.9(v)), can be used when evaluating the series. …