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 Yearling
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Feb
25
revised Asymptotic form of the integral $\int_{0}^{\infty} dx ~ \sqrt{x^2 + wx} ~ e^{-ixs}$ for $s \to \infty$
edited body
Feb
25
comment Asymptotic form of the integral $\int_{0}^{\infty} dx ~ \sqrt{x^2 + wx} ~ e^{-ixs}$ for $s \to \infty$
Regarding the sign: as you most probably well know the sign of the sqrt-operation is ambiguous as the function is multivalued in a complex setting. We need to take the branch which is analytically connected to $\sqrt{x^2 + wx}>0$ in the original integral when rotating the contour to the lower half plane.
Feb
25
comment Asymptotic form of the integral $\int_{0}^{\infty} dx ~ \sqrt{x^2 + wx} ~ e^{-ixs}$ for $s \to \infty$
@glance: yes you need Re$(s)>0$ in the rotated integral. However, afterwards to can analytically continue the result to understand that it coincides with the original integral whenever the latter converges.
Feb
25
revised Asymptotic form of the integral $\int_{0}^{\infty} dx ~ \sqrt{x^2 + wx} ~ e^{-ixs}$ for $s \to \infty$
edited body
Feb
25
comment Asymptotic form of the integral $\int_{0}^{\infty} dx ~ \sqrt{x^2 + wx} ~ e^{-ixs}$ for $s \to \infty$
@glance: Sorry, that was a typo.
Feb
19
awarded  Yearling
Feb
10
comment Prove that $\sin x<x$, if $x>0$
I would believe that already for $x>1$ the inequality is obvious.
Feb
7
comment Residue Theorem for Laplace Transform
There is actually also a website explaining the detailed steps: lmgtfy.com/?q=inverse+laplace+residue.
Feb
7
answered Evaluating $\lim_{h \to 0}\frac{(x+h)^{\frac15}-x^{\frac15}}{h}$
Feb
7
revised How do I prove this trigonometric integral inequality?
added 22 characters in body
Feb
7
answered How do I prove this trigonometric integral inequality?
Feb
6
comment Minimal polynomial of a matrix satisfying $A^t=A^2$
@fvel: I believe $t$ indicates the transpose...
Feb
6
comment integration by parts transforming a vector integral to vector times divergence?
I'm not sure your identity is correct. Maybe you did a mistake copying it?
Feb
6
comment integration by parts transforming a vector integral to vector times divergence?
As far as I remember, Jackson has a long list of vector identities close to the back and front cover of his bock.
Feb
3
comment How can I calculate the integral $ \int_{\left| z \right| = r} \frac{dz}{(z-a)^n(z-b)^n} $
Why the question in the title does not match the one in the remainder?
Feb
2
comment Gradient of product and inverse matrix
Is the gradient with respect to $x$?
Feb
2
comment Integration of fraction
@Tyrone: the first comment was rather general. If you read it carefully, you understand that the problem is exactly not that it does not make sense (your question makes perfectly sense). With the second, I did imply that I would be surprised if this question did come up in some application but again not that the question does not make any sense. By the way, I am not one of the downvoters.
Feb
2
comment Integration of fraction
Not anything which can be formulated in terms of mathematics is a good question in the sense that answering it will provide insights.
Feb
2
comment $f(z)=\bar{z}$ has no primitive
+1: for spelling out what we mean by an antiderivative and showing an alternative approach.
Feb
2
answered $f(z)=\bar{z}$ has no primitive