let be the analytic everywhere function f(x) with limit tending to +oo and -oo with oo0 infinite then we want to calculate the integral..(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int_{0}^{\infty}dxe^{-x^{2}}=0.5\sqrt{\pi}[/tex]

ot do so we expand the exponential function into a power series (we can do it as the function is analytic everywhere) so we have...

[tex]exp(-x^2)=\sum_{n=0}^{\infty}a_{n}x^{n}[/tex]

but the integral of this power series is divergent in the form:

[tex]\sum_{n=0}^{\infty}a_{n}(\infty)^{n} [/tex]

wich is clearly infinite...so where is the solution to this paradox?..thanks.

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# A paradox?

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