sign change of x

ThU — Fri, 22 Feb 2013 03:39:24 Z

Hi, maybe you could set algsubs(x=-x,term);

and then apply asympt.

Need to subs x= -x on both input and output

Carl Love — Fri, 22 Feb 2013 05:12:02 Z

Use this procedure:

asympt_neg:= (f,x)-> subs(x= -x, asympt(subs(x= -x, f), x, _rest));

A good function to test this on is GAMMA (because GAMMA is not an even function and it has a nontrivial asymptotic series):

asympt_neg(GAMMA(x), x);

You can view the results yourself. You can see that there are a number of differences between this series and the regular asypmtotic series for GAMMA (which is probably the most famous of all nontrivial asymptotic series). If you evaluate this series at, say, -9.5, you'll see that it gives an excellent approximation to GAMMA(-9.5), and a much better approximation than the regular series gives.

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sign change of x

Need to subs x= -x on both input and output