Carleman's Inequality
Let 
be a Set of Positive numbers. Then the Geometric Mean and ArithmeticMean satisfy
Here, the constant e is the best possible, in the sense that counterexamples can be constructed for anystricter Inequality which uses a smaller constant.See also Arithmetic Mean, e, Geometric Mean
References
Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, p. 1094, 1979. Hardy, G. H.; Littlewood, J. E.; and Pólya, G. Inequalities, 2nd ed. Cambridge, England: Cambridge University Press, pp. 249-250, 1988.
- Sprague-Grundy Function
- Sprague-Grundy Number
- Sprague-Grundy Value
- Spread (Link)
- Spread (Tree)
- Spun Knot
- Squarable
- Square
- Square Bracket Polynomial
- Square Cupola
- Square Curve
- Square Cutting
- Squared
- Squared Square
- Square-Free
- Squarefree
- Butterfly Catastrophe
- Butterfly Curve
- Butterfly Effect
- Butterfly Fractal
- Butterfly Polyiamond
- Butterfly Theorem
- Bäcklund Transformation
- Bézier Curve
- Bézier Spline