Logarithmically Convex Sequence

A logarithmically convex sequence (or log-convex sequence) is a sequence ${a_n}$ of nonnegative real numbers for which

at every applicable index. A positive sequence is logarithmically convex iff its successive quotients form a nondecreasing sequence. For example, the factorial sequence is logarithmically convex.

See also

Logarithmically Concave Sequence, Logarithmically Convex Function, Partition Function Q

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References

Guo, H. and Zhang, Z.-R. "The Log-Convexity of the

-th Root Sequence of the Distinct Partition Function." Elec. J. Combin. 33, No. 3, P3.50, 1-22, 2026. https://doi.org/10.37236/14748.

Cite this as:

Weisstein, Eric W. "Logarithmically Convex Sequence." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LogarithmicallyConvexSequence.html

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