Re: [Axiom-developer] 20080427.01.tpd.patch (CATS Schaums-Axiom equivalence testing (29-34))

[Martin Rubey]

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:

> 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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