#17970: implement Meijer G function
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Reporter: rws | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.6
Component: symbolics | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by rws:
Old description:
> 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.
> }}}
>
> Mpmath has numerics too.
>
> https://en.wikipedia.org/wiki/Meijer_G-function
New description:
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.
}}}
Mpmath has numerics too.
https://en.wikipedia.org/wiki/Meijer_G-function
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Ticket URL: <http://trac.sagemath.org/ticket/17970#comment:1>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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