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## Re: [Axiom-developer] Re: About Schaums.

 From: Martin Rubey Subject: Re: [Axiom-developer] Re: About Schaums. Date: 30 Apr 2008 19:52:59 +0200 User-agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.4

```root <address@hidden> writes:
>   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

```