I'm expanding a function in chebyshev polynomials and then substituting
it into a differential equation. I get an expression that has noun forms
for the derivatives. I would like to expand the derivatives without
having maxima expand the chebyshev polynomials into their basic form.
How can I make it do this?
Example, I want to get %o199 where the derivatives have been evaluated
according to the gradef properties of the chebyshev polynomials, not
into a form that's a basic polynomial in x (apologies for the word
wrapping in the last expression).
----
(%i196) depends(foo,x);
(%o196) [foo(x)]
(%i197) foo = sum(A[i]*funmake(chebyshev_t,[i,x]),i,0,3);
(%o197) foo = A T (x) + A T (x) + A T (x) + A T (x)
3 3 2 2 1 1 0 0
(%i198) 'diff(foo,x)-3*'diff(foo,x,2) = 0;
2
dfoo d foo
(%o198) ---- - 3 ----- = 0
dx 2
dx
(%i199) subst(%th(2),%th(1));
d
(%o199) -- (A T (x) + A T (x) + A T (x) + A T (x))
dx 3 3 2 2 1 1 0 0
2
d
- 3 (--- (A T (x) + A T (x) + A T (x) + A T
(x))) = 0
2 3 3 2 2 1 1 0 0
dx
(%i200)