Opened 7 years ago

Last modified 3 years ago

#17970 new defect

implement Meijer G function

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

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Description (last modified by rws)

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

Change History (3)

comment:1 Changed 7 years ago by rws

  • Description modified (diff)

comment:2 Changed 3 years ago by rws

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

comment:3 Changed 3 years ago by vdelecroix

  • Milestone changed from sage-8.3 to sage-8.4

update milestone 8.3 -> 8.4

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