MittagLefflerE
MittagLefflerE[α,z]
gives the Mittag–Leffler function .
MittagLefflerE[α,β,z]
gives the generalized Mittag–Leffler function .
Details

- MittagLefflerE is a mathematical function, suitable for both symbolic and numerical manipulation.
- MittagLefflerE allows
to be any positive real number.
- The generalized Mittag–Leffler function is an entire function of
given by its defining series
.
- The Mittag–Leffler function
is equivalent to
.
Examples
open allclose allBasic Examples (5)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Series expansion at Infinity:
Scope (22)
Numerical Evaluation (4)
Specific Values (4)
Simple exact values are generated automatically:
Find a value of x for which MittagLefflerE[1/2,x]=0.5:
Visualization (3)
Plot the MittagLefflerE function for noninteger orders:
Plot MittagLefflerE function for integer orders:
Function Properties (7)
is defined for all
as long as
:
The complex domain of MittagLefflerE is the same:
MittagLefflerE has the mirror property :
MittagLefflerE threads elementwise over lists:
MittagLefflerE is an analytic function for :
Differentiation (2)
Series Expansions (2)
Find the Taylor expansion using Series:
Applications (1)
Text
Wolfram Research (2012), MittagLefflerE, Wolfram Language function, https://reference.wolfram.com/language/ref/MittagLefflerE.html.
CMS
Wolfram Language. 2012. "MittagLefflerE." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MittagLefflerE.html.
APA
Wolfram Language. (2012). MittagLefflerE. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MittagLefflerE.html