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 Sep30 revised Why does being holomorphic imply so much about a function? added 367 characters in body Sep27 accepted Can I use the residue calculus here? Sep27 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. Sep27 comment Rationalise $\frac{2}{\sqrt{12}}$ fully and $$\frac{\sqrt{12}}{6}=\frac{\sqrt{3\times 4}}{6}=\frac{2\sqrt{3}}{6}=\frac{\sqrt{3}}{3}.$$ Sep27 accepted A question on the Wronskian Sep27 asked A question on the Wronskian Sep26 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. Sep26 answered Why does being holomorphic imply so much about a function? Sep26 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. Sep26 comment Can I use the residue calculus here? @ Jack D'Aurizio I don't think that substitution works... Sep26 revised Can I use the residue calculus here? added 205 characters in body Sep26 reviewed Approve Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$ Sep26 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. Sep26 asked Can I use the residue calculus here? Sep25 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 Sep25 answered There is at most one way to represent a number as $a+b\sqrt 2$ with rational $a,b$ Sep25 revised Find the first derivative $y=\sqrt\frac{1+\cosθ}{1-\cosθ}$ added 254 characters in body Sep24 awarded Autobiographer Sep23 revised Bounds on the real and imaginary parts of the digamma function $\psi$ deleted 12 characters in body Sep23 reviewed Approve Derivation of Steepest Descent Direction used in Line Search Methods