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]]. | ||
| Line 7: | Line 7: | ||
==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)= | + | * {{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^2)=cos(z)}}: $(2.3)$ (uses notation $E_2$ instead of $E_{2,1}$) |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Revision as of 21:31, 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
- H.J. Haubold, A.M. Mathai and R.K. Saxena: Mittag-Leffler Functions and Their Applications (2011)... (previous)... (next): $(2.3)$ (uses notation $E_2$ instead of $E_{2,1}$)
