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Sep
30
awarded  Explainer
Sep
30
reviewed Approve How to proof the following function is always constant which satisfies $f\left( x \right) + a\int_{x - 1}^x {f\left( t \right)\,dt} $?
Sep
30
revised Why does being holomorphic imply so much about a function?
added 367 characters in body
Sep
27
accepted Can I use the residue calculus here?
Sep
27
comment Can I use the residue calculus here?
Thanks. I think you're right about the semi-circular contour. I also tried the box contour, and a similar problem arises. Maybe the residue calculus can't be used here.
Sep
27
comment Rationalise $\frac{2}{\sqrt{12}}$ fully
and $$\frac{\sqrt{12}}{6}=\frac{\sqrt{3\times 4}}{6}=\frac{2\sqrt{3}}{6}=\frac{\sqrt{3}}{3}.$$
Sep
27
accepted A question on the Wronskian
Sep
27
asked A question on the Wronskian
Sep
26
comment Why does being holomorphic imply so much about a function?
@Shakespeare The proof of the CR equations begins by thinking about all the possible directions. It can, however, be shown that the CR equations cover all such cases.
Sep
26
answered Why does being holomorphic imply so much about a function?
Sep
26
comment Can I use the residue calculus here?
@ Jack D'Aurizio I see what you mean now. However, I don't think this translates well from your original statement "replace $x$ with $\frac{1}{\log\log t}$." From that I get $t=e^{e^{1/x}}$, which gives $t=e$ for both $x=\pm\infty$, making the lower and upper bounds of the integral the same. Thanks for clarifying. +1.
Sep
26
comment Can I use the residue calculus here?
@ Jack D'Aurizio I don't think that substitution works...
Sep
26
revised Can I use the residue calculus here?
added 205 characters in body
Sep
26
reviewed Approve Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
Sep
26
comment Can I use the residue calculus here?
@ Claude Leibovici I am curious as I have seen other problems of this type, and have never computed an inifinite double sum of residues before.
Sep
26
asked Can I use the residue calculus here?
Sep
25
revised There is at most one way to represent a number as $a+b\sqrt 2$ with rational $a,b$
added 4 characters in body
Sep
25
answered There is at most one way to represent a number as $a+b\sqrt 2$ with rational $a,b$
Sep
25
revised Find the first derivative $y=\sqrt\frac{1+\cosθ}{1-\cosθ}$
added 254 characters in body
Sep
24
awarded  Autobiographer