Opened 7 years ago

Last modified 7 months ago

#17970 new defect

implement Meijer G function

Reported by: rws Owned by:
Priority: major Milestone: sage-8.4
Component: symbolics Keywords: meijerg
Cc: slelievre Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description (last modified by tmonteil)

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[0](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?
Object `meijerg` not found.

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.

https://en.wikipedia.org/wiki/Meijer_G-function

See also https://ask.sagemath.org/question/60006/meijer-g-function-in-sage/

Change History (6)

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
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