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Proceedings of the American Mathematical Society

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

 

 

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: 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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DOI: https://doi.org/10.1090/S0002-9939-1970-0257412-X
Keywords: Elliptic integrals, inequalities, ellipsoid, capacity, duplication theorem, hypergeometric $ R$-functions
Article copyright: © Copyright 1970 American Mathematical Society