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4h
comment Is $74*2^n - 1$ prime for some $n$?
@hardmath : and that is a problem because ... ?
7h
comment Show that the closed ball $B[x,1]$ in $c_0$ is not compact.
I mean find a set such that each point in the set has distance $> 2/3$ from each other point in the set.
20h
comment What is meant by “Each of two concentric discs has 20 radial sections of equal size”
Hint: after a random rotation, what is the expected number of matching sectors?
1d
comment For which $x$ the inequality $ax+be^{x/2}>c$, where $a,b,c,x>0$ and $c>2b$ holds
Duplicate of math.stackexchange.com/questions/1300048/…
1d
comment Differential equation for the logistic map
Of course, there's no hope of a good approximation unless (1) is in the region of parameter space where the nonzero fixed point is stable.
1d
comment Differential equation for the logistic map
Just reverse the steps to go from the $y$ equation to the $x$ differential equation.
1d
comment Differential equation for the logistic map
For one thing, the left side in (1) is $x_{n+1}$, the value of the population at the next iteration, while the left side in (2) is $x'(t)$, the rate of change of the population at time $t$.
1d
comment Differential equation for the logistic map
Yes, the recurrence and the differential equation are very different.
1d
comment Ignoring the pole?
Then you'd have an improper integral that does not converge. It would exist at most in the Cauchy principal value sense.
1d
comment Ignoring the pole?
The contour is the circle $|z|=3$ that you're integrating over. $|-2| \ne 3$ so $-2$ is not on the contour.
1d
comment Ignoring the pole?
No, you don't have $\int_0^{2\pi} \dfrac{z}{z+2}\; dz$, you have $\displaystyle \oint_C \dfrac{z}{z+2}\; dz$ where $C$ is the (positively oriented, I presume) circle $|z|=3$. $z$ doesn't go anywhere near $0$ or $2\pi$.
1d
comment Can something contain iteself?
If you want to ask a mathematical question, it helps to know precisely what you mean by the question.
1d
comment How is the degree of a polynomial defined? $a_1+a_2x^2+\cdots+a_nx^{n-1}$ has degree $n$ or $n-1$?
More precisely, it is $n-1$ if the coefficient of $x^{n-1}$ is nonzero.
1d
comment Can something contain iteself?
That is, a set cannot contain itself as a member. It can (and does) contain itself as a subset.
1d
comment Simplifying cyclometric function
It is not a semicircle. In particular, it is not an algebraic function of $x$.
May
22
comment Evaluating $ \int_0^\theta \cosh(a\sin x) dx$
@Dr.SonnhardGraubner Did you mean the value at $\pi$, or the fact the antiderivative is non-elementary? The value at $\pi$ is "well-known", the non-elementary antiderivative comes from the Risch theory.
May
22
comment Binomial distribution central moment calculation
Thanks for catching that. Edited it.
May
21
comment What is the sample rate?
You' might have to give more context if you want us to understand what you're asking. What data? Sampling how?
May
21
comment Evaluate determinant of an $n \times n$ matrix, help
This is the case $n=4$. The case $n=5$ would be $$\pmatrix{1 & 1 & 0 & 0 & 0\cr 1 & 1 & 1 & 0 & 0\cr 0 & 1 & 1 & 1 & 0\cr 0 & 0 & 1 & 1 & 1\cr 0 & 0 & 0 & 1 & 1\cr}$$
May
21
comment Evaluate determinant of an $n \times n$ matrix, help
Do you not see the pattern? You have $1$'s on the main diagonal and the diagonals immediately above and below that, everything else $0$. The fourth row is $[0,0,1,1,1,0,\ldots,0]$.