Difference between revisions of "Mittag-Leffler"
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(Created page with "The Mittag-Leffler function $E_{\alpha, \beta}$ is defined by the series $$E_{\alpha, \beta}(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{z^k}{\Gamma(\alpha k + \beta)},$$ where...") |
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| − | The Mittag-Leffler function $E_{\alpha, \beta}$ is defined by the series | + | The Mittag-Leffler function $E_{\alpha, \beta}$ is defined for $z, \alpha, \beta \in \mathbb{C}$ with $\mathrm{Re}(\alpha), \mathrm{Re}(\beta) > 0$ by the series |
$$E_{\alpha, \beta}(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{z^k}{\Gamma(\alpha k + \beta)},$$ | $$E_{\alpha, \beta}(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{z^k}{\Gamma(\alpha k + \beta)},$$ | ||
where $\Gamma$ denotes the [[gamma]] function. | where $\Gamma$ denotes the [[gamma]] function. | ||
Revision as of 16:47, 2 January 2018
The Mittag-Leffler function $E_{\alpha, \beta}$ is defined for $z, \alpha, \beta \in \mathbb{C}$ with $\mathrm{Re}(\alpha), \mathrm{Re}(\beta) > 0$ by the series $$E_{\alpha, \beta}(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{z^k}{\Gamma(\alpha k + \beta)},$$ where $\Gamma$ denotes the gamma function.
