# Mittag-Leffler

Are Mittag-Leffler function implemented in Sagemath ?

Mittag-Leffler

Are Mittag-Leffler function implemented in Sagemath ?

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2

There does not seem to be an implementation in Sage.

There is an implementation in R in the **MittagLeffleR** R package.

- Home: https://strakaps.github.io/MittagLeffleR/
- Reference manual: https://strakaps.github.io/MittagLeffleR/reference/
- Cran page: https://cran.r-project.org/web/packages/MittagLeffleR/.
- Documentation on Cran: https://cran.r-project.org/web/packages/MittagLeffleR/MittagLeffleR.pdf

It can be used from Sage.

To install this R package for Sage's R, run this in a terminal:

```
$ sage --R
```

Then at the R prompt (`>`

) type:

```
> install.packages('MittagLeffleR')
```

and choose a download mirror in the numbered list.

Once the installation is complete, quit R:

```
> q()
```

Next time you launch Sage:

```
$ sage
```

you can load the MittagLeffleR R package:

```
sage: r.library('MittagLeffleR')
```

Then you can run commands such as:

```
sage: r('mlf(2, 0.7)')
[1] 20.96643
sage: r('dml(1, 0.8)')
[1] 0.2557438
sage: r('dml(1, 0.6, second.type=TRUE)')
[1] 0.4832354
sage: r('pml(2, 0.7, 1.5)')
[1] 0.6597308
sage: r('qml(p = c(0.25, 0.5, 0.75), tail = 0.6, scale = 100)')
[1] 11.64327 60.56854 284.67928
sage: r('rml(10, 0.7, 1)')
[1] 2.863445e-01 2.189476e+00 1.013715e+00 2.465789e+00 4.260511e-01
[6] 4.568785e-01 7.676349e-02 6.497517e-05 5.912041e-01 5.403624e-01
```

Here is a Mittag-Leffler function based on that:

```
def mittag_leffler(z, a, b=1, g=1):
r"""
Return the Mittag-Leffler function for these arguments.
"""
r.library('MittagLeffleR')
return r(f'mlf({z}, {a}, b={b}, g={g})').sage()
```

Usage:

```
sage: mittag_leffler(2, 0.7)
20.966433131482
```

In the same vein :

```
sage: mathematica.MittagLefflerE?
Signature: mathematica.MittagLefflerE(*args, **kwds)
Type: MathematicaFunction
String form: MittagLefflerE
File: /usr/local/sage-9/src/sage/interfaces/mathematica.py
Docstring:
MittagLefflerE[α, z] gives the Mittag–Leffler function E (z).
α
MittagLefflerE[α, β, z] gives the generalized Mittag–Leffler function
E (z).
α, β
```

which uses either a local Mathematica install or the (gratis, if not free) Wolfram engine.

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Asked: ** 2022-07-20 14:12:22 +0100 **

Seen: **142 times**

Last updated: **Jul 24 '22**

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