Levin transformations

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1: 3.9 Acceleration of Convergence

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§3.9(v) Levin’s and Weniger’s Transformations

►We give a special form of Levin’s transformation in which the sequence $s=\{s_n\}$ of partial sums $s_n={\sum }_{j=0}^n{a}_j$ is transformed into: …Sequences that are accelerated by Levin’s transformation include logarithmically convergent sequences, i. …

2: 2.11 Remainder Terms; Stokes Phenomenon

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Table 2.11.1: Whittaker functions with Levin’s transformation.

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$n$	$a_n$	$s_n$	$d_n$
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… ►shows that this direct estimate is correct to almost 3D. ►The fourth column of Table 2.11.1 gives the results of applying the following variant of Levin’s transformation: …

3: 3.5 Quadrature

… ►Convergence acceleration schemes, for example Levin’s transformation (§3.9(v)), can be used when evaluating the series. …

4: Bibliography L

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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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External Links:

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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External Links:

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

Referenced by:

§18.32.

Encodings:

BibTeX

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Algorithm 344: Student’s t-distribution [S14]. Comm. ACM 12 (1), pp. 37–38.

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Notes:

Single-precision Fortran, maximum accuracy 8S. For Remarks see same journal 13(1970), pp. 124 and 449.

External Links:

ISSN 0001-0782, Document, Remark 1 and Remark 2

Referenced by:

§8.28(iv).

Encodings:

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On the theory of diffraction by an aperture in an infinite plane screen. I. Phys. Rev. 74 (8), pp. 958–974.

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External Links:

Document, MathReview (C. J. Bouwkamp), ZentralBlatt

Referenced by:

§11.12.

Encodings:

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Bessel transforms and rational extrapolation. Numer. Math. 47 (1), pp. 1–14.

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External Links:

ISSN 0029-599X, Document, MathReview (Vítĕzslav Veselý), ZentralBlatt

Referenced by:

§10.74(vii).

Encodings:

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