Difference between revisions of "Glaisher–Kinkelin constant"
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(Created page with "The Glaisher–Kinkelin constant is defined by the formula $$A=\displaystyle\lim_{n \rightarrow \infty} \dfrac{(2\pi)^{\frac{n}{2}}n^{\frac{n^2}{2}-\frac{1}{12}}e^{-\frac{3n^2...") |
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The Glaisher–Kinkelin constant is defined by the formula | The Glaisher–Kinkelin constant is defined by the formula | ||
| − | $$A=\displaystyle\lim_{n \rightarrow \infty} \dfrac{(2\pi)^{\frac{n}{2}}n^{\frac{n^2}{2}-\frac{1}{12}}e^{-\frac{3n^2}{4}+\frac{1}{12}}}{G(n+1)} | + | $$A=\displaystyle\lim_{n \rightarrow \infty} \dfrac{(2\pi)^{\frac{n}{2}}n^{\frac{n^2}{2}-\frac{1}{12}}e^{-\frac{3n^2}{4}+\frac{1}{12}}}{G(n+1)},$$ |
| + | where $G$ is the [[Barnes G|Barnes $G$]] function. | ||
=Properties= | =Properties= | ||
| − | + | [[Derivative of zeta at -1]]<br /> | |
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 16:01, 16 June 2016
The Glaisher–Kinkelin constant is defined by the formula $$A=\displaystyle\lim_{n \rightarrow \infty} \dfrac{(2\pi)^{\frac{n}{2}}n^{\frac{n^2}{2}-\frac{1}{12}}e^{-\frac{3n^2}{4}+\frac{1}{12}}}{G(n+1)},$$ where $G$ is the Barnes $G$ function.
