Bug in quadgk on an infinite domain
Marco Caliari
marco.caliari at univr.it
Tue Jun 9 07:30:52 CDT 2009
Dear maintainers,
there is a bug in the 'Standard Infinite to finite integral
transformation' in quadgk.m (3.2.0). The correct transformation is
## g(t) = t / (1 - t^2)
## g'(t) = (1 + t^2) / (1 - t^2) ^ 2
With the enclosed patch, I get
octave:1> quadgk(@(x)exp(-x.^2),-10,10)
ans = 1.77245385090546e+00
octave:2> quadgk(@(x)exp(-x.^2),-Inf,Inf)
ans = 1.77245385078031e+00
that is sqrt(pi)
octave:3> sqrt(pi)
ans = 1.77245385090552e+00
whereas, with the original quadgk, I get
octave:4> quadgk(@(x)exp(-x.^2),-Inf,Inf)
ans = 1.15710256465273e+00
Best regards,
Marco
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