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Re: [Axiom-developer] 20080427.01.tpd.patch (CATS Schaums-Axiom equivale

 From: Martin Rubey Subject: Re: [Axiom-developer] 20080427.01.tpd.patch (CATS Schaums-Axiom equivalence testing (29-34)) Date: 30 Apr 2008 21:54:32 +0200 User-agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.4

I investigated a tiny bit further, but only to notice that this result is
*not* produced by the pattern matcher, but rather by the general integration
algorithm.

I'm a bit worried.

Martin

Martin Rubey <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
>
>
>
>
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