svanshaar wrote:
> I am trying to numerically evaluate the integral of bessel functions.
> I've tried constructing it various ways. The one that makes most
> sense to me is:
> a=var('a')
> f=bessel_J(1,a)*bessel_J(0,0.1*a)*e^(-5*a)
> f.numerical_integral(a,0,infinity)
>
> I get the error: Cannot evaluate symbolic expression to a numeric
> value.
>
> I also tried placing various arguments inside n() functions. Then I
> get the error: self must be a numeric expression
>
> Obviously, if I don't have a variable in my expression, I wouldn't
> need Sage to help me integrate it. I get the same errors with
> nintegral() instead of numerical_integral().
>
> How do I construct this to get a numeric result?
>
sage: def f(x): return bessel_J(1,x)*bessel_J(0,0.1*x)*e^(-5*x)
....:
sage: numerical_integral(f, 0, oo)
(0.019408449962002559, 1.5271811488988928e-10)
sage: numerical_integral(lambda x:
bessel_J(1,x)*bessel_J(0,0.1*x)*e^(-5*x), 0>
(0.019408449962002559, 1.5271811488988928e-10)
You can also use scipy and several other systems to do the numeric
integration. The problem here is that bessel_J is not a symbolic
function, and does not know how to deal with symbolic variables. It
would be great if someone submitted a patch to take care of this!
Thanks,
Jason
--
Jason Grout
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