Difference between revisions of "E(1,1)(z)=exp(z)"

From specialfunctionswiki
Jump to: navigation, search
 
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 |z|<1|next=E(2,1)(z)=cosh(sqrt(z))}}: $(2.2)$ (uses notation $E_1$ instead of $E_{1,1}$)
+
* {{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))}}: $(2.2)$ (uses notation $E_1$ instead of $E_{1,1}$)
  
 
[[Category:Theorem]]
 
[[Category:Theorem]]
 
[[Category:Unproven]]
 
[[Category:Unproven]]

Latest revision as of 21:34, 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