> From: Dieter Kaiser
>
> Today, I had a long search for a subtle and small bug.
I hope it wasn't me. I have been extending, documenting
and testing the lambert_w code this week.
I was impressed that with a couple of lines of code for the
'integral property, and without touching code elsewhere,
maxima now knows:
(%i1) integrate(diff(f(x),x)*lambert_w(f(x)),x);
2
f(x) (lambert_w (f(x)) - lambert_w(f(x)) + 1)
(%o1) ---------------------------------------------
lambert_w(f(x))
> I have found a further and easy extension to the integrator
> to get more integrals for special functions. I have tried it
> and got nice results.
Great. I am happy to do some detailed coding and testing for
special functions. I was looking at your new code last night
- trying to work out how to integrate Jacobi elliptic functions.
I didn't find a neat, general solution but it looked feasible.
I was also wondering how to add a hook/property to integrate
(simple) expressions containing a special function, such as:
* integrate( sin(x)/x, x)
* integrate( x^(n+1).bessel_j(n,x), x)
* integrate( jacobi_sn(u,m)^n, dx)
If we could search the expression for special functions and
have a general, table-driven way of trying custom integration
routines. Perhaps an 'integral-hook (or some better name)
property on %sin, %bessel_j .... that returns points to
a function with specialized knowledge.
David
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