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Cauchy principal value integral

asked 2021-10-15 22:29:46 +0100

hicheme gravatar image

updated 2021-10-18 17:27:18 +0100

FrédéricC gravatar image

How can I calculate a Cauchy principal Value integral with sagemath

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answered 2021-10-16 00:32:22 +0100

tmonteil gravatar image

I do not know much about the notion of Cauchy principal value integral, but you can reproduce the two examples given on Wikipedia https://en.wikipedia.org/wiki/Cauchy_... :

sage: a = SR.var('a')
sage: assume(0<2*a<1)
sage: f = integral(1/x, x, -1, -2*a) + integral(1/x, x, a, 1)
sage: f.limit(a=0)
log(2)

and

sage: a = SR.var('a')
sage: assume(a>0)
sage: f = integral(2*x/(x^2-1), x, -2*a, a)
sage: f.limit(a=oo)
-2*log(2)
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Asked: 2021-10-15 22:29:46 +0100

Seen: 47 times

Last updated: Oct 18