E(2,1)(-z^2)=cos(z)
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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.
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 $E_{2,1}$)
