The function x |-> -gamma_incomplete(1/4,x^4)*x/(4*abs(x)) is not continuous at zero. To do
the calculation correctly, you need to consider the intervals (-inf,0) and (0, inf) separately.
Doing that, the definite integral is correct, I think.
Sometime ago, I wrote a bit of code that attempts to determine when an expression is continuous. I know
that in general this is algorithmically impossible--I was aiming for a satisficing (good enough) method.
--Barton
-----maxima-bounces at math.utexas.edu wrote: -----
I get this incorrect result for the following calculations:
?
(%i4) kill(all);
?
(%o0) done
(%i1) exp(-x^4);
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(%o1) %e^-x^4
(%i2) integrate(%o1,x,minf,inf);
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(%o2) gamma(1/4)/2
(%i3) integrate(%o1,x);
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(%o3) -gamma_incomplete(1/4,x^4)*x/(4*abs(x))
(%i4) limit(%o3,x,inf)-limit(%o3,x,minf);
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(%o4) 0
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The limit should give the same answer as the more direct definite integral.? I can’t take the analysis much further because I know very little about the gamma_incomplete function.? It looks like a bug.
?
Rich
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