Re: f( x + O(x) ) or f(x) + O(x) ?

[Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>]

* Bill Allombert [2021-02-20 17:17]:
> On Sat, Feb 20, 2021 at 03:36:37PM +0000, Jacques Gélinas wrote:
> > In a previous post, I used this oneliner to get the vector of 
> > Maclaurin coefficients of a function:
> > 
> > maclv(f,k) = Vec( f( x+O(x^(k+1)) ) );
> > 
> > The boundary case k=0 should return f(0) as in
> > maclv( cosh, 0) == [1]
> > maclv( sinc,  0) == [1]
> > 
> > But this yields an incorrect result for this modified Riemann Xi function,
> > 
> > Xi(x) = my(s=1/2+x); Pi^(-s/2)*gamma(1+s/2)*(s-1)*zeta(s);
> 
> zeta is wrong:
> 
> ? zeta(1/2+x+O(x))
> %32 = -1.9884831127532564396510949587415908792*x+O(x^2)
> ? zeta(1/2+x+O(x^2))
> %33 = -1.4603545088095868128894991525152980125-3.9226461392091517274715314467145995137*x+O(x^2)
> 
> The real bug is
> 
> ? 1 + O(x) == O(x)
> %1 = 1

Now fixed in 'master'. Thanks !

Cheers,

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite de Bordeaux         Fax: (+33) (0)5 40 00 21 23
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