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1d
comment Cauchy's Residue Theorem contradiction?
@robjohn While I guess you can say that, talking about "residues of sets" is not standard terminology.
1d
answered Cauchy's Residue Theorem contradiction?
1d
revised Describe set of $z^2$ as $z$ moves over 2nd quadrant and show it is open and connected
added 77 characters in body; edited tags; edited title
2d
answered Trouble with an inequality between magnitudes of complex numbers
2d
comment How to conclude this proof that real and imaginary parts of holomorphic functions are harmonic.
As I wrote: $\dfrac{\partial \bar f}{\partial z} = \overline{\dfrac{\partial f}{\partial \bar z}}$ which is $0$ since $f$ is holomorphic.
2d
comment Test if a number is in ${\mathbb R}$
What operations do you allow? I doubt the question is answerable without more information.
2d
comment Bounds on function $\exp(-\frac{1}{2}x^2)$
To get a good answer, you should probably tell us what you want to use the bounds for. Showing convergence of some integral? Estimating the error function? Something else?
2d
revised How to conclude this proof that real and imaginary parts of holomorphic functions are harmonic.
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2d
answered How to conclude this proof that real and imaginary parts of holomorphic functions are harmonic.
Feb
9
comment Volume of a 'cylinder with rounded sides'
A torus isn't really "made out of something by drilling a hole", so it's hard to say exactly what you're looking for? Ellipsoids perhaps.
Feb
7
revised Rudin's RCA, Chapter 2 Definitions
edited tags
Feb
5
revised How to prove $\lim_{s \rightarrow \infty} \zeta(s) = 1$?
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Feb
5
comment How to prove $\lim_{s \rightarrow \infty} \zeta(s) = 1$?
$\zeta$ is usually studied as a function of a complex variable, but $\zeta(s)$ doesn't have a limit as $s \to \infty$ as a complex number (since $\zeta$ has an essential singularity at $\infty$).
Feb
5
revised How to prove $\lim_{s \rightarrow \infty} \zeta(s) = 1$?
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Feb
5
answered How to prove $\lim_{s \rightarrow \infty} \zeta(s) = 1$?
Feb
5
comment How to prove $\lim_{s \rightarrow \infty} \zeta(s) = 1$?
What do you consider basic? (If you're interested in the $\zeta$-function, integrals should definitely be on the list of basic things.)
Feb
5
answered Prove this integral is analytic
Feb
5
comment Prove Complex Limits from first principle definition
What on earth is "$z > i$" supposed to mean?
Jan
31
answered Prove Complex analysis inequality
Jan
31
answered Eigenvector and eigenvalue for exponential matrix