Difference between revisions of "E(2,1)(z)=cosh(sqrt(z))"

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(Created page with "==Theorem== The following formula holds: $$E_{2,1}(z)=\cosh(\sqrt{z}),$$ where $E_{2,1}$ denotes the Mittag-Leffler function and $\cosh$ denotes cosh. ==Proof== ==Re...")
 
 
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==Theorem==
 
==Theorem==
The following formula holds:
+
The following formula holds for $z \in \mathbb{C}$:
 
$$E_{2,1}(z)=\cosh(\sqrt{z}),$$
 
$$E_{2,1}(z)=\cosh(\sqrt{z}),$$
 
where $E_{2,1}$ denotes the [[Mittag-Leffler]] function and $\cosh$ denotes [[cosh]].
 
where $E_{2,1}$ denotes the [[Mittag-Leffler]] function and $\cosh$ denotes [[cosh]].
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==References==
 
==References==
* {{PaperReference|Mittag-Leffler Functions and Their Applications|2011|H.J. Haubold|author2=A.M. Mathai|author3=R.K. Saxena|prev=E (0,1)(z)=1/(1-z) for abs(z) less than 1|next=E(2,1)(z)=cosh(sqrt(z))}}: $(2.1)$ (uses notation $E_1$ instead of $E_{1,1}$)
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* {{PaperReference|Mittag-Leffler Functions and Their Applications|2011|H.J. Haubold|author2=A.M. Mathai|author3=R.K. Saxena|prev=E(1,1)(z)=exp(z)|next=E(2,1)(-z^2)=cos(z)}}: $(2.3)$ (uses notation $E_2$ instead of $E_{2,1}$)
  
 
[[Category:Theorem]]
 
[[Category:Theorem]]
 
[[Category:Unproven]]
 
[[Category:Unproven]]

Latest revision as of 21:33, 2 January 2018

Theorem

The following formula holds for $z \in \mathbb{C}$: $$E_{2,1}(z)=\cosh(\sqrt{z}),$$ where $E_{2,1}$ denotes the Mittag-Leffler function and $\cosh$ denotes cosh.

Proof

References