[Top][All Lists]
[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Re: [Axiom-developer] Re: About Schaums.
From: |
root |
Subject: |
Re: [Axiom-developer] Re: About Schaums. |
Date: |
Wed, 30 Apr 2008 17:09:35 -0400 |
>> Axiom has a closed form for 2 integrals where Schaums has series.
>
>But at least one of them seems to be wrong. Since it seems that my message was
>overlooked, I repeat it here:
>
>address@hidden writes:
>
>> 14:668 SCHAUMS AND AXIOM DIFFER (Axiom has closed form)
>
>But I'm not so sure that it is correct, at least not for a=1 and x in 0..1.
>
>draw(D(integrate(asech(x)/x,x),x)-asech(x)/x, x=0..1)
>
>I'm an absolute nobody on this stuff, so I may well be missing something. On
>the other hand, the power series for (asech x)/x + (log x - log 2)/x is
>Dfinite:
>
>(76) -> guessPRec [coefficient(series normalize((asech x + log x - log 2) /
>x)::GSERIES(EXPR INT, x, 0), i) for i in 0..30]
>
> (76)
> [
> [
> function =
> BRACKET
> f(n):
> 2 2 1
> (n + 6n + 9)f(n + 2) + (- n - 3n - 2)f(n)= 0,f(0)= 0,f(1)= - -
> 4
> ,
> order= 0]
> ]
> Type: List Record(function: Expression Integer,order: NonNegativeInteger)
>
>and this doesn't agree at all with the power series you get from
>D(integrate(asech(x)/x,x),x).
>
>Should be investigated,
Martin,
I saw your note but haven't yet had the time to prove the result
one way or the other. I just finished the last integrals and did a
bug-catching, "check my homework" review last night. I plan to use
the 3 Ms to check both Axiom and Schaums. Ultimately, I suspect they
are both "right" under some as-yet-unstated set of assumptions.
But I have much more to learn about branch cuts, which ones are
assumed, and how they propagate before I think I have a solid clue.
These assumptions should really be written down someplace but they
are not.
Tim