835 reputation
414
bio website
location
age
visits member for 2 years, 9 months
seen yesterday

2d
accepted Calculate $I_m = \int_{-\infty}^\infty \frac{dx}{1+x+x^2+\cdots+x^{2m}}$ using complex variables
2d
comment Calculate $I_m = \int_{-\infty}^\infty \frac{dx}{1+x+x^2+\cdots+x^{2m}}$ using complex variables
Lightbulb moment. Of course. Thank you!
2d
comment Calculate $I_m = \int_{-\infty}^\infty \frac{dx}{1+x+x^2+\cdots+x^{2m}}$ using complex variables
How do you get from $\left(e^{-i8\pi/5} - e^{-i6\pi/5} + e^{-i16\pi/5} - e^{-i12\pi/5}\right)$ to $\left(e^{i2\pi/5} - e^{i4\pi/5} + e^{i4\pi/5} - e^{-i2\pi/5}\right)$?
Dec
16
asked Calculate $I_m = \int_{-\infty}^\infty \frac{dx}{1+x+x^2+\cdots+x^{2m}}$ using complex variables
Dec
15
accepted What conditions are necessary on $a,b,c,d$ so that the Mobius transformation $w=\frac{az-b}{cz-d}$ has only one fixed point?
Dec
15
comment What conditions are necessary on $a,b,c,d$ so that the Mobius transformation $w=\frac{az-b}{cz-d}$ has only one fixed point?
@DanielFischer, on your last question, no. I am only assuming that $ad-bc \neq 0$. I thought the "standard" definition of a Mobius transform implied that $a,b,c,d \in \mathbb{R}$ -- I guess I'm mistaken on this point. Also, I would be happy to upvote your comments if you were interested in submitting them as an answer (since you are addressing my question directly).
Dec
15
comment What conditions are necessary on $a,b,c,d$ so that the Mobius transformation $w=\frac{az-b}{cz-d}$ has only one fixed point?
@DanielFischer The reason I believe it should lie in $\mathbb{R}$ is because $a,b,c,d \in \mathbb{R}$. If there is only one fixed point, then (if I'm right) the discriminant is zero and what remains is in $\mathbb{R}$. I think the only way for a complex number to "arise" is if the discriminant < 0. I could be mistaken.
Dec
15
asked What conditions are necessary on $a,b,c,d$ so that the Mobius transformation $w=\frac{az-b}{cz-d}$ has only one fixed point?
Dec
14
accepted Let $z_1$, $z_2$ and $z_3$ be complex vertices of an equilateral triangle. Show $z_1^2 + z_2^2 + z_3^2 = z_1 z_2 + z_2 z_3 + z_3 z_1$.
Dec
14
asked Let $z_1$, $z_2$ and $z_3$ be complex vertices of an equilateral triangle. Show $z_1^2 + z_2^2 + z_3^2 = z_1 z_2 + z_2 z_3 + z_3 z_1$.
Dec
14
comment Compute $\int_0^\infty \frac{dx}{x^5+1}$ using a contour in the upper half complex plane that encloses one of the roots of $z^5+1=0$
Thanks at least for confirming my suspicion that the hint was incorrect.
Dec
14
asked Compute $\int_0^\infty \frac{dx}{x^5+1}$ using a contour in the upper half complex plane that encloses one of the roots of $z^5+1=0$
Dec
14
awarded  Benefactor
Dec
14
comment Describe the Riemann surface for $w=z^2-1$.
thank you for a lucid explanation!
Dec
13
accepted How can I show that $u=e^{\sigma\sqrt{\Delta t}}$ in the binomial option pricing model
Dec
12
comment Describe the Riemann surface for $w=z^2-1$.
Can you explain or go into some detail as to why this choice of cut makes sense? I am having a difficult time visualizing how the cut would work..
Dec
12
revised What is the angle at critical point $z=1$ of $\left|z-\frac{i-1}{2}\right|=\frac{\sqrt{5}}{\sqrt{2}}$ under the Joukowski transform?
added attempted solution
Dec
12
accepted Describe the Riemann surface for $w=z^2-1$.
Dec
12
asked What is the angle at critical point $z=1$ of $\left|z-\frac{i-1}{2}\right|=\frac{\sqrt{5}}{\sqrt{2}}$ under the Joukowski transform?
Dec
12
comment Describe the Riemann surface for $w=z^2-1$.
Does the multivalued nature of the function, and hence the necessity of the riemann surface, follow from the fact that the inverse of the function is multivalued?