Difference between revisions of "E(1,1)(z)=exp(z)"
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(Created page with "==Theorem== The following formula holds: $$E_{1,1}(z)=e^z,$$ where $E_{1,1}$ denotes the Mittag-Leffler function and $e^z$ denotes the exponential. ==Proof== ==Refer...") |
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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 (0,1)(z)=1/(1-z) for |z|<1|next=E(2,1)(z)=cosh(sqrt(z))}}: $(2. | + | * {{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 |z|<1|next=E(2,1)(z)=cosh(sqrt(z))}}: $(2.2)$ (uses notation $E_1$ instead of $E_{1,1}$) |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Revision as of 21:29, 2 January 2018
Theorem
The following formula holds: $$E_{1,1}(z)=e^z,$$ where $E_{1,1}$ denotes the Mittag-Leffler function and $e^z$ denotes the exponential.
Proof
References
- H.J. Haubold, A.M. Mathai and R.K. Saxena: Mittag-Leffler Functions and Their Applications (2011)... (previous)... (next): $(2.2)$ (uses notation $E_1$ instead of $E_{1,1}$)
