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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Inequalities for a symmetric elliptic integral


Author: B. C. Carlson
Journal: Proc. Amer. Math. Soc. 25 (1970), 698-703
MSC: Primary 33.19
DOI: https://doi.org/10.1090/S0002-9939-1970-0257412-X
MathSciNet review: 0257412
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Abstract | References | Similar Articles | Additional Information

Abstract: Inequalities are found for an incomplete elliptic integral of the first kind which represents the reciprocal of the capacity of an ellipsoid with semiaxes $x,\;y,\;z$. One sequence of symmetric algebraic functions of $x,\;y,\;z$ converges to the value of the integral from below and two from above. Among the elements of these sequences are upper and lower approximations due to Pólya and Szegö.


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Keywords: Elliptic integrals, inequalities, ellipsoid, capacity, duplication theorem, hypergeometric <IMG WIDTH="21" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$R$">-functions
Article copyright: © Copyright 1970 American Mathematical Society