| Jacques Gélinas on Sat, 20 Feb 2021 16:36:44 +0100 |
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| 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