Difference between revisions of "Airy zeta function"
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| − | The [[Airy | + | The [[Airy Ai | Airy function]] $\mathrm{Ai}$ is oscillatory for negative values of $x$. This yields a sequence of zeros $\{a_i\}_{i=1}^{\infty}$. We define the Airy zeta function using these zeros in the following way: |
$$\zeta_{\mathrm{Ai}}(z) = \displaystyle\sum_{k=1}^{\infty} \dfrac{1}{|a_k|^z}.$$ | $$\zeta_{\mathrm{Ai}}(z) = \displaystyle\sum_{k=1}^{\infty} \dfrac{1}{|a_k|^z}.$$ | ||
| − | + | ||
| − | + | =Properties= | |
| + | [[Airy zeta function at 2]]<br /> | ||
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=References= | =References= | ||
| − | [ | + | * {{PaperReference|On the quantum zeta function|1996|Richard E. Crandall}} |
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| + | [[Category:SpecialFunction]] | ||
Latest revision as of 02:16, 2 November 2016
The Airy function $\mathrm{Ai}$ is oscillatory for negative values of $x$. This yields a sequence of zeros $\{a_i\}_{i=1}^{\infty}$. We define the Airy zeta function using these zeros in the following way: $$\zeta_{\mathrm{Ai}}(z) = \displaystyle\sum_{k=1}^{\infty} \dfrac{1}{|a_k|^z}.$$
