Hello Alasdair,
I'm not expert in canonical Maxima but
(%i13) subst(u-x=h,taylor(f(u),u,x,3));
(%o13) f(x)+h^3*('at('diff(f(u),u,3),u = x))/6
+h^2*('at('diff(f(u),u,2),u = x))/2+h*('at('diff(f(u),u,1),u
= x))
(%i14) subst(u-x=h,taylor(sin(u),u,x,3));
(%o14) -h^2*sin(x)/2+sin(x)-h^3*cos(x)/6+h*cos(x)
is quite simple, and gives reasonable results for explicit as well as
litteral functions.
I don't know if maxima knows of a simpler way of writing f^(5)(x)
(fifth derivative at x) than
('at('diff(f(u),u,5),u = x))
Eric
Le 05/02/2012 05:08, Alasdair McAndrew a ?crit :
> What is the canonical Maxima way of obtaining the series form
>
> f(x) + hf'(x) + h^2f''(x)/2 + h^3f'''(x)/6 + ...
>
> for f(x+h)?
>
> Thanks,
> Alasdair
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