Abel summability

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1: 1.15 Summability Methods

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Abel Summability

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Cesàro Summability

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Abel Means

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Abel Summability

► ${\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}f(t)dt$ is Abel summable to $L$, or …

2: 22.18 Mathematical Applications

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§22.18(iv) Elliptic Curves and the Jacobi–Abel Addition Theorem

… ►For any two points $(x_1,y_1)$ and $(x_2,y_2)$ on this curve, their sum $(x_3,y_3)$, always a third point on the curve, is defined by the Jacobi–Abel addition law …a construction due to Abel; see Whittaker and Watson (1927, pp. 442, 496–497). …

3: 2.10 Sums and Sequences

… ►Another version is the Abel–Plana formula: … ►

The first infinite integral in (2.10.2) converges.

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4: Bibliography 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:

BibTeX

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5: Bibliography W

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Tables of Summable Series and Integrals Involving Bessel Functions. Holden-Day, San Francisco, CA.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§10.22(vi), §10.23(iv), §10.43(vi).

Encodings:

BibTeX

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6: 1.13 Differential Equations

… ►Then the following relation is known as Abel’s identity …

7: 10.65 Power Series

… ►For further power series summable in terms of Kelvin functions and their derivatives see Hansen (1975).

8: Bibliography S

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Large orders and summability of eigenvalue perturbation theory: A mathematical overview. Int. J. Quantum Chem. 21, pp. 3–25.

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External Links:

Document

Referenced by:

§22.19(ii).

Encodings:

BibTeX

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9: Bibliography B

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Abelian Functions: Abel’s Theorem and the Allied Theory of Theta Functions. Cambridge University Press, Cambridge.

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Notes:

Reprint of the 1897 original, with a foreword by Igor Krichever.

External Links:

ISBN 0-521-49877-5, MathReview (John B. Little), ZentralBlatt

Referenced by:

§20.9(ii).

Encodings:

BibTeX

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10: 1.2 Elementary Algebra

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§1.2(iv) Means

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