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11h
revised Book recommendation for a new student on complex analysis
deleted 1 character in body
Jun
30
awarded  Yearling
Jun
27
comment Existence of unique circle passing through interior points of unit disk meeting the boundary orthogonally
@DavidC.Ullrich Thanks for your patience. I'm working on applying this to the problem itself. I am guessing I need to come up with the appropriate diameter of the unit circle applicable to the given pair $a,b$ and the circle it determines. Maybe map the chord to a parallel diameter.
Jun
27
accepted Existence of unique circle passing through interior points of unit disk meeting the boundary orthogonally
Jun
27
comment Existence of unique circle passing through interior points of unit disk meeting the boundary orthogonally
Thanks very much. I am busy working things out. It looks very convenient , as you say.
Jun
27
comment Existence of unique circle passing through interior points of unit disk meeting the boundary orthogonally
Dear Will - Thank you for your guidance. As you can see above, I am struggling with the kind help I am receiving from Prof. Ulrich. Even if I get no further, maybe you would please elaborate a bit as to why the upper half plane would be advantageous. Regards,
Jun
27
comment Existence of unique circle passing through interior points of unit disk meeting the boundary orthogonally
@DavidC.Ulrich Dear Professor - Please forgive me for being so incredibly dense. I can't think of another circle that goes through $0$ and $1$ that meets the unit circle at right angles. The circle centered at $x=1/2$ above that meets these criteria would have its center at $i\infty$? I truly apologize for my lack of insight.
Jun
26
comment Existence of unique circle passing through interior points of unit disk meeting the boundary orthogonally
@DavidC.Ullrich the $x$-axis between $0$ and $1$ looks like the diameter of the circle centered at $x=1/2$ and the radius of the unit circle. So it would be perpendicular to the inner circle and the unit circle at $x=1$. Does that constitute a proof of the hint?
Jun
26
asked Existence of unique circle passing through interior points of unit disk meeting the boundary orthogonally
Jun
14
comment $\int_{\gamma}f(z)\log\left(\frac{z+1}{z-1}\right)dz = 2\pi i\int_{x=-1}^{x=1}f(x)dx$ on an ellipse
Thanks Ron. You know what I think of you.
Jun
14
accepted $\int_{\gamma}f(z)\log\left(\frac{z+1}{z-1}\right)dz = 2\pi i\int_{x=-1}^{x=1}f(x)dx$ on an ellipse
Jun
14
asked $\int_{\gamma}f(z)\log\left(\frac{z+1}{z-1}\right)dz = 2\pi i\int_{x=-1}^{x=1}f(x)dx$ on an ellipse
Jun
12
awarded  Nice Answer
Jun
10
comment What is a nice way to compute $f(x) = x / (\exp(x) - 1)$?
Dear Pedro - Please forgive this if it's a dopy question. Would you please show how to derive your recursive formula - $\sum_{k<n} =0$ from the generating function relation, which is my typical starting point. Thanks. Regards,
Jun
7
revised Why $\zeta(-2) $ is not $\sum_{n=1}^{\infty}\frac{1}{n^{-2}}$?
edited title
Jun
3
revised Best Sets of Lecture Notes and Articles
added 117 characters in body
Jun
2
comment how to check this function is not complex differentiable in 0
Dear Prof. Blatter - I had upvoted this a short while ago. Maybe I could impose on you for an efficient way to show f(z) satisfies the C-R equations at $z=0$. Thanks and regards,
May
31
comment Show that a map $f:X\to Y$ is onto iff $f(f^{-1}(C))=C$ for all subsets $C\subseteq Y$.
Thanks - big help.
May
30
comment Show that a map $f:X\to Y$ is onto iff $f(f^{-1}(C))=C$ for all subsets $C\subseteq Y$.
Maybe I could ask you: following your hint, if $c\in$ LHS, then there was an $x\in X$ s.t. it is also in $f^{-1}(C))$ so that $f(c) \in C$. But since at this point, "onto" is not assumed, what is the meaning of $f^{-1}(C)$. Thanks. Regards,
May
17
comment Integral evaluation $\int_{-\infty}^{\infty}\frac{\cos (ax)}{\pi (1+x^2)}dx$
Thanks very much. Whatever the motivation, it's a pleasure to watch you in action.