Difference between revisions of "E(2,1)(-z^2)=cos(z)"
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(Created page with "==Theorem== The following formula holds for $z \in \mathbb{C}$: $$E_{2,1}(-z^2)=\cos(z),$$ where $E_{2,1}$ denotes the Mittag-Leffler function and $\cos$ denotes [[cosine]...") |
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==Theorem== | ==Theorem== | ||
The following formula holds for $z \in \mathbb{C}$: | The following formula holds for $z \in \mathbb{C}$: | ||
| − | $$E_{2,1}(-z^2)=\cos(z),$$ | + | $$E_{2,1}\left(-z^2\right)=\cos(z),$$ |
where $E_{2,1}$ denotes the [[Mittag-Leffler]] function and $\cos$ denotes [[cosine]]. | where $E_{2,1}$ denotes the [[Mittag-Leffler]] function and $\cos$ denotes [[cosine]]. | ||
Latest revision as of 21:55, 2 January 2018
Theorem
The following formula holds for $z \in \mathbb{C}$: $$E_{2,1}\left(-z^2\right)=\cos(z),$$ where $E_{2,1}$ denotes the Mittag-Leffler function and $\cos$ denotes cosine.
Proof
References
- H.J. Haubold, A.M. Mathai and R.K. Saxena: Mittag-Leffler Functions and Their Applications (2011)... (previous)... (next): $(2.4)$ (uses notation $E_2$ instead of $E_{2,1}$)
