Difference between revisions of "Airy zeta function at 2"
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(Created page with "==Theorem== The following formula holds: $$\zeta_{\mathrm{Ai}}(2)=\dfrac{3^{\frac{5}{3}}\Gamma^4(\frac{2}{3})}{4\pi^2},$$ where $\zeta_{\mathrm{Ai}}$ denotes the Airy Ai,...") |
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The following formula holds: | The following formula holds: | ||
$$\zeta_{\mathrm{Ai}}(2)=\dfrac{3^{\frac{5}{3}}\Gamma^4(\frac{2}{3})}{4\pi^2},$$ | $$\zeta_{\mathrm{Ai}}(2)=\dfrac{3^{\frac{5}{3}}\Gamma^4(\frac{2}{3})}{4\pi^2},$$ | ||
| − | where $\zeta_{\mathrm{Ai}}$ denotes the [[Airy | + | where $\zeta_{\mathrm{Ai}}$ denotes the [[Airy zeta function]], $\Gamma$ denotes the [[gamma]] function, and $\pi$ denotes [[pi]]. |
==Proof== | ==Proof== | ||
Latest revision as of 02:20, 2 November 2016
Theorem
The following formula holds: $$\zeta_{\mathrm{Ai}}(2)=\dfrac{3^{\frac{5}{3}}\Gamma^4(\frac{2}{3})}{4\pi^2},$$ where $\zeta_{\mathrm{Ai}}$ denotes the Airy zeta function, $\Gamma$ denotes the gamma function, and $\pi$ denotes pi.
