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11: 19.24 Inequalities

… ►Approximations and one-sided inequalities for $R_G(0,y,z)$ follow from those given in §19.9(i) for the length $L(a,b)$ of an ellipse with semiaxes $a$ and $b$, since …

12: Bibliography

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Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, $\pi$, and the Ladies Diary. Amer. Math. Monthly 95 (7), pp. 585–608.

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External Links:

ISSN 0002-9890, FullText, Document, MathReview (R. A. Askey), ZentralBlatt

Referenced by:

§19.9(i).

Encodings:

BibTeX

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13: 18.18 Sums

… ►Let $f(z)$ be analytic within an ellipse $E$ with foci $z=\pm 1$, and …

14: Bibliography B

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Inequalities for the perimeter of an ellipse. J. Math. Anal. Appl. 260 (2), pp. 295–306.

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External Links:

ISSN 0022-247X, Document, MathReview (Matti Vuorinen), ZentralBlatt

Referenced by:

§19.9(i).

Encodings:

BibTeX

…

15: 3.11 Approximation Techniques

… ►If $x$ is replaced by a complex variable $z$ and $f(z)$ is analytic, then the expansion (3.11.11) converges within an ellipse. …