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#3314 Maxima does not calculate taylor series in some cases.
Maxima does not calculate Taylor series in some cases. For instance:
assume(x>0);
define(g(t),(cos(t)-1)/t^2);
define(f(x),integrate(g(t),t,0,x));
ratsimp(taylor(f(x),x,0,12)-(sum(limit(diff(f(x),x,n),x,0)/n!*x^n,n,0,12)));
Here you have more cases like this:
g(t),sin(t)^2/t^2-1
g(t),sin(t)/t
g(t),(sin(t)/t)^2
g(t),(exp(t^2)-1)/t
g(t),(cos(t)-1)/t^2
g(t),(sin(t)^2-t^2)/t^3
It seems that, instead of Taylor series for int_0^x, it calculates Taylor series for int_x^{2x}
I have only found this bug when calculating Taylor series for functions f defined as in the example (by means of an integral).
wxMaxima version: 15.8.2
Maxima version: 5.37.2
Maxima build date: 2015-10-30 02:08:33
Host type: x86_64-unknown-linux-gnu
System type: BSD BSD NIL
Lisp implementation type: GNU Common Lisp (GCL)
Lisp implementation version: GCL 2.6.12
.-----------------------------------------------------------
How we got the wrong result. Some details.
(%i3) assume(x>0);
define(g(t),h(t)/t^2);
define(f(x),integrate(g(t),t,0,x));
(%o1) [x>0]
(%o2) g(t):=h(t)/t^2
(%o3) f(x):=integrate(h(t)/t^2,t,0,x);
(%i4) T:taylor(f(x),x,0,3);
(T) h(0)/x+(5(at('diff(h(x),x,1),x=0)))/6+((at('diff(h(x),x,2),x=0))x)/2+((at('diff(h(x),x,3),x=0))x^2)/4+
(7(at('diff(h(x),x,4),x=0))*x^3)/72+...
(%i7) h(t):=cos(t)-1;
ev(T, nouns);
expand(%);
(%o5) h(t):=cos(t)-1
(%o6)/R/ (7x^3-36x)/72
(%o7) (7*x^3)/72-x/2
How we got the wrong result. Some details.
(%i3) assume(x>0);
define(g(t),h(t)/t^2);
define(f(x),integrate(g(t),t,0,x));
(%o1) [x>0]
(%o2) g(t):=h(t)/t^2
(%o3) f(x):=integrate(h(t)/t^2,t,0,x);
(%i4) T:taylor(f(x),x,0,3);
(T)
h(0)/x+(5(at('diff(h(x),x,1),x=0)))/6+((at('diff(h(x),x,2),x=0))x)/2+((at('diff(h(x),x,3),x=0))x^2)/4+(7(at('diff(h(x),x,4),x=0))*x^3)/72+...
(%i7) h(t):=cos(t)-1;
ev(T, nouns);
expand(%);
(%o5) h(t):=cos(t)-1
(%o6)/R/ (7x^3-36x)/72
(%o7) (7*x^3)/72-x/2
2017-06-30 16:59 GMT+03:00 APRILIO aprilio@users.sf.net: