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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.