Luboš Motl
Reputation
6,195
Next privilege 10,000 Rep.
Access moderator tools
 Jun 11 revised Question about Holomorphic functions added 159 characters in body; added 780 characters in body Jun 11 comment Question about Holomorphic functions Pleasure. Maths is trivial - once it's proved. ;-) Jun 11 answered Question about Holomorphic functions Jun 10 comment p chance of winning tennis point -> what f(p) chance of winning game? Thanks for the great edits, @Chris! You're a co-author. ;-) That's exactly what I saw in Mathematica. Jun 10 revised p chance of winning tennis point -> what f(p) chance of winning game? added 352 characters in body Jun 10 answered p chance of winning tennis point -> what f(p) chance of winning game? Jun 10 answered Integral of $\sqrt{1+\tan^2x}$ Jun 10 answered Applications of systems of linear equations Jun 10 answered evaluating a complex integral where the integrand is analytic within the contour but not necessarily analytic on the contour Jun 10 answered How to find remainder modulo $n$, when $n$ is a large number Jun 10 answered How to find the triangle matrix of a given matrix? Jun 10 revised Is fourier series of a function with $e^{j\theta}$ replaced with a complex variable $z$ holomorphic on the unit disc? added 587 characters in body; added 97 characters in body; added 118 characters in body Jun 10 answered Is fourier series of a function with $e^{j\theta}$ replaced with a complex variable $z$ holomorphic on the unit disc? Jun 10 comment Finding power series representation of $\int_0^{\frac{\pi }{2}} \frac{1}{\sqrt {1 - k^2\sin^2{x}}}\;{dx}$ Sorry, @Asaf, where did you get the factor of $1/3$? What does it mean? Jun 10 comment Finding power series representation of $\int_0^{\frac{\pi }{2}} \frac{1}{\sqrt {1 - k^2\sin^2{x}}}\;{dx}$ Be careful, if it is an exam problem and they will mechanically compare the result with a wrong official template, they may declare your correct answer incorrect and you will have to defend yourself - for which, I believe, you have all the weapons. Jun 10 comment Question about direct sum of function space Dear @vonjd, your problem already starts with ${\mathbb R}^3$: the first sentence says that $V$ itself are functions from $U$ which is a subset of ${\mathbb R}^3$. $V$ itself are functions that take value in ${\mathbb R}$ and $V\oplus V\oplus V$ are functions from ${\mathbb R}^3$ to another ${\mathbb R}^3$. But functions from ${\mathbb R}$ never appear in your problem at all so I don't understand in what sense it would be "natural". Real numbers and their 3rd power are equally natural but only the latter appear in your problem. The tripling only affects the value of the function not the domain Jun 10 awarded Enlightened Jun 10 comment Finding power series representation of $\int_0^{\frac{\pi }{2}} \frac{1}{\sqrt {1 - k^2\sin^2{x}}}\;{dx}$ It's just a small digit "2" that someone missed, but you didn't. Maybe they thought it was a mark for a footnote. ;-) Jun 10 revised Finding power series representation of $\int_0^{\frac{\pi }{2}} \frac{1}{\sqrt {1 - k^2\sin^2{x}}}\;{dx}$ added 329 characters in body; added 1 characters in body Jun 10 comment Finding power series representation of $\int_0^{\frac{\pi }{2}} \frac{1}{\sqrt {1 - k^2\sin^2{x}}}\;{dx}$ Oh, I eventually noticed that it's actually the same thing. In that case, I am sure that your result is correct. In the original formula, the whole big ratio in the parentheses should be squared, otherwise it's correct.