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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
answered Evaluating $ \int_0^\theta \cosh(a\sin x) dx$
May
22
answered Extreme values of a continuous function on a closed connected domain …
May
22
comment Binomial distribution central moment calculation
Thanks for catching that. Edited it.
May
22
revised Binomial distribution central moment calculation
edited body
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
answered Binomial distribution central moment calculation
May
21
answered Normal Family complex
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 $[0,0,1,1,1,0,\ldots,0]$.
May
21
answered Polynomials and Commutativity
May
21
answered Creative way to find this area
May
21
revised The dimension of centralizer of a Matrix.
added 104 characters in body
May
21
answered The dimension of centralizer of a Matrix.
May
21
comment System of linear equations: and a small perturbation
"Choose $x$ to maximize ..." means find $x$ with $\|x\| = 1$ that gives the largest possible value of $\|Ax\|/\|x\|$. You can do this (assuming we're using the Euclidean norm on vectors) by taking $x$ to be an eigenvector of $A^T A$ for its largest eigenvalue. Similarly, $y$ will be an eigenvector of $(A^{-1})^T A^{-1}$ for its largest eigenvalue.
May
21
comment Find an example of a sequence not in $l^1$ satisfying certain boundedness conditions.
Maple tells me $a_n = 2\,{\frac {{\it LaguerreL} \left( n,2 \right) -{\it LaguerreL} \left( n,1,2 \right) }{n}} $ for $n \ge 1$.
May
21
comment Find an example of a sequence not in $l^1$ satisfying certain boundedness conditions.
The series is $f(z) = e^{-1} \sum_{n=0}^\infty a_n z^n$ where $a_n =\displaystyle \sum_{k=0}^n \dfrac{(-2)^k}{k!} {n-1 \choose n-k}$.
May
21
answered System of linear equations: and a small perturbation
May
21
comment Counting Coprime Numbers in a range:
Rather than bothering to factor $n$, if $b - a$ is small enough to do that you might as well just compute $\gcd(n,x)$ for each $x$ in the interval.
May
21
comment Counting Coprime Numbers in a range:
The inclusion-exclusion method for the number coprime to $n$ in $[1,k]$ gives you $$T(n,k) = \sum_{d \mid n} \mu(d) \lfloor k/d \rfloor $$ which is OEIS sequence A078401 (for $k \le n$).