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## 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:
>
>
>>   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

```