Opened 7 years ago

# implement Meijer G function

Reported by: Owned by: rws major sage-8.4 symbolics meijerg slelievre N/A

This function would allow to express the result from differentiation of several special functions with respect to the order parameter, which at the moment gives an error:

```sage: diff(exp_integral_e(n,x),n)
NotImplementedError: The derivative of this function is only implemented for
sage: gamma_inc(n,x).diff(n)
D(gamma)(n, x)

sage: sympy.expint(n, x).diff(n)
-x**(n - 1)*meijerg(((), (1, 1)), ((0, 0, -n + 1), ()), x)
sage: sympy.uppergamma(n, x).diff(n)
meijerg(((), (1, 1)), ((0, 0, n), ()), x) + log(x)*uppergamma(n, x)
sage: sympy.lowergamma(n, x).diff(n)
-meijerg(((), (1, 1)), ((0, 0, n), ()), x) - log(x)*uppergamma(n, x) + gamma(n)*polygamma(0, n)
sage: meijerg?

sage: laplace(cos(-1/t), t, s, algorithm='sympy')
...
AttributeError: Unable to convert SymPy result (=meijerg(((), ()), ((-1/2, 0, 1/2), (0,)), s**2/16)/4) into Sage
```

Mpmath has numerics too.

### comment:1 Changed 7 years ago by rws

• Description modified (diff)

### comment:2 Changed 4 years ago by rws

• Description modified (diff)
• Milestone changed from sage-6.6 to sage-8.3

### comment:3 Changed 4 years ago by vdelecroix

• Milestone changed from sage-8.3 to sage-8.4

update milestone 8.3 -> 8.4

### comment:4 Changed 8 months ago by tmonteil

• Description modified (diff)

### comment:6 Changed 7 months ago by gh-sheerluck

```sage: integrate(x * bessel_Y(1, x), (x, 0 ,1), algorithm="sympy")
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
/usr/lib/python3.10/site-packages/sage/interfaces/sympy.py in _sympysage_function_by_name(fname)
303         else:
304             # the function defined in sympy is not known in sage
--> 305             raise AttributeError(fname)
306     return func
307

AttributeError: meijerg
```
Note: See TracTickets for help on using tickets.