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

[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