You may be right - my University Maple 16 gets the right answer, but my
17beta does not. I've reported this as a Maple beta bug.
On Tuesday, 27 August 2013 06:34:07 UTC+1, Georgi Guninski wrote:
>
> Thank you for the note.
>
> You claim: "For \int_{1/3}^1 fra(1/x) dx Maple returns ln 3 - 1/3".
Thank you for the note.
You claim: "For \int_{1/3}^1 fra(1/x) dx Maple returns ln 3 - 1/3".
I can't reproduce this on Maple 13 on linux,
here is a session:
> fra1:=x->1/2+I/(2*Pi)*log(-exp(-2*Pi*I*x)):
> ii:=int(fra1(1/x),x=1/3..1);
ii := - 5/6 + ln(3)
>
What abou
Well, after full simplification fra1() no longer equals {x}:
sage: ex=fra1(x).full_simplify()
sage: ex
x
It is more interesting to me how Maple finds the correct integral with {x}.
Played with int_a^b f(x,{x}) =? int_a^b f(x,fra1(x))
Whenever Maple could compute the definite integral, it equals
Well, the derivative of the fractional part is indeed 1 where it is
defined, as
lim((fra(x+eps)-fra(x))/eps)=lim(eps/eps)=1 unless adding eps crosses a
boundary,
which it won't do for eps small enough.
Maxima (5.29) returns (4 pi log 2 + i log(-1) +pi)/(4 pi).
Depending on the value of log(-1),
