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Jacques Gélinas on Sat, 20 Feb 2021 16:36:44 +0100
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f( x + O(x) ) or f(x) + O(x) ?
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- To: "pari-users@pari.math.u-bordeaux.fr" <pari-users@pari.math.u-bordeaux.fr>
- Subject: f( x + O(x) ) or f(x) + O(x) ?
- From: Jacques Gélinas <jacquesg00@hotmail.com>
- Date: Sat, 20 Feb 2021 15:36:37 +0000
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- Thread-topic: f( x + O(x) ) or f(x) + O(x) ?
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);
maclv(Xi,0) != maclv(Xi,1)[1] \\ 0.67690 instead of 0.49712, *** oups!!
However, Vec( Xi(x) + O(x) ) does give the correct answer here, [0.49712].
Can I have an explanation or (better) advice regarding this behaviour of GP ?
Jacques Gélinas
Ref: http://pari.math.u-bordeaux.fr/archives/pari-users-1908/msg00022.html