K-function

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The $K$-function is defined by $$K(z)=(2\pi)^{\frac{1-z}{2}} \exp \left[ {z \choose 2}+\displaystyle\int_0^{z-1} \log(\Gamma(\xi+1)) \mathrm{d}\xi \right],$$ where $\pi$ denotes pi, $\exp$ denotes the exponential, ${z \choose 2}$ denotes the binomial coefficient, $\log$ denotes the logarithm, and $\Gamma$ denotes the gamma function.

Properties[edit]

Hyperfactorial in terms of K-function

References[edit]