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N.B. A detailed on-line essay by S. Finch was the starting point for this entry.
Consider the sum
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(1) |
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(2) |
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(3) |
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(4) |
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(5) |
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(6) |
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(7) |
A modified sum was considered by Elbert (1973):
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(8) |
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(9) |
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(10) |
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(11) |
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(12) |
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(13) |
See also Convex Hull
References
Drinfeljd, V. G. ``A Cyclic Inequality.'' Math. Notes. Acad. Sci. USSR 9, 68-71, 1971.
Elbert, A. ``On a Cyclic Inequality.'' Period. Math. Hungar. 4, 163-168, 1973.
Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/shapiro/shapiro.html
Mitrinovic, D. S.; Pecaric, J. E.; and Fink, A. M. Classical and New Inequalities in Analysis. New York: Kluwer, 1993.
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© 1996-9 Eric W. Weisstein