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Apr
16
comment A sufficient condition to ensure $\alpha=\beta$
Source? Motivation? Effort? Close.
Apr
16
comment For what values of x does it converge?
What do you mean by "character"? Do you mean, for what values of $x$ does it converge? Where did you come across this series?
Apr
16
comment series involving $\log \left(\tanh\frac{\pi k}{2} \right)$
What do you mean, "how to approach this series using Jacobi Theta Function"? Do you mean, how to prove the equalities in the display? Where did you "find" this series? Was there no information there?
Apr
16
comment Filtering matrices based on model
Let's look at a simpler problem, with $1\times2$ matrices, which we can interpret as points in the plane. So, you're given hundreds of points in the plane, and you want to know which one "looks the most like" some given point. I don't see how you can pssibly do that without calculating the distance from each point to the model point, and then finding the smallest of these distances. You might be able to save a little time by, say, sorting the points on the first coordinate, but you still have to do heaps of computation.
Apr
16
comment Finding a horizontal line of intersection of a function under the constraint that the area between the intersection points equals a specified value.
If $f$ has a closed-form antiderivative, $F(x)=\int f(x)\,dx$, then (at least in the two-intersection case) it reduces to solving the pair of equations, $f(x_1)=f(x_2)$, $F(x_2)-F(x_1)=c$.
Apr
16
comment Find the least possible value for $n$
Source? Motivation? Effort? Close.
Apr
16
revised Vandermonde's Identity : Summations with binomial coefficients
typo in title
Apr
16
answered Why do prime numbers in modulo result in more uniform distributions?
Apr
16
comment Why do prime numbers in modulo result in more uniform distributions?
Have you seen the closed form formula for $S_n$?
Apr
16
revised The Starry Rebound
edited tags
Apr
16
comment The Starry Rebound
The question has turned up on various websites, going back at least to 2005, but I haven't seen any answers. Is it really homework? It should have an additional tag. I'll edit in "probability", but if someone has a better tag idea, go for it.
Apr
16
comment Suppose $x$, $y$, and $z$ are integers that satisfy the system equations
I don't see how the first equation in the (3) implies the second.
Apr
16
revised How would you prove $\sum_{i=1}^{n} (3/4^i) < 1$ by induction?
more informative title
Apr
16
revised How to prove the binomial coefficient identity $\binom{n}{c}+ \binom{n}{c+1}= \binom{n+1}{c+1}$ by induction?
more informative title
Apr
16
comment Suppose $x$, $y$, and $z$ are integers that satisfy the system equations
Unsourced, unmotivated, no evidence of any thought/work on part of OP --- not the best usage of this website.
Apr
16
revised Suppose $x$, $y$, and $z$ are integers that satisfy the system equations
edited tags
Apr
16
revised Why is an irrational number's algebraic complexity the opposite of its Diophantine complexity?
expansion
Apr
16
comment Help understanding fields.
1) The list in the answer omits associativity. 2) (as noted in the preceding comment) the list omits distributivity. 3) Item 4 in the list doesn't recognize that the additive identity has no multiplicative inverse.
Apr
16
comment Coefficient of specific term in a Series Expansion
Brian, Sol has $z^3$ where you have $z$, and (judging from the comment on my answer) that seems to be a stumbling block for Sol.
Apr
16
comment Coefficient of specific term in a Series Expansion
Sol, if you introduce a new variable $Q$, defined by $Q=-z^3$, then your function becomes $(1-Q)^{-n}$, and the binomial theorem applies; after applying it, you can then replace $Q$ everywhere with $-z^3$ to get an answer involving $z$.