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Results tagged with divergent-integrals
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user 11260
2
votes
Where do these divergent integrals appear in mathematics and physics?
Perhaps the most "famous" divergent integral in physics is the Casimir vacuum energy of the electromagnetic field,
$$\int_0^\infty x^2\sqrt{1+x^2}\,dx"="-\frac{1}{10},$$
and the related class of integ …
- 188k
6
votes
How do I solve the following definite integral (preferably by an asymptotic method)?
Here is a log-log plot of
$$\delta I=I_{\text{appr}}-\int_{1}^{\infty} \frac{\sin^2 (\mu \sqrt{x^2 -1})}{(x+1)^{\frac{9}{2}} (x-1)^{\frac{3}{2}}} \,dx,$$
as a function of $\mu$, with
$$I_{\text{appr}} …
- 188k