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12h
comment Find a function with the property, or prove it doesn't exist
Your property, as written, doesn't make much sense. What kind of a variable is $a$, and what does $c_1,c_2,\ldots,c_n$ mean? Note that $f$ can only be partially differentiated with respect to its own variables $x_1$, $\ldots$, $x_n$.
16h
answered Evaluate $\sin\left(-\frac{\pi}{6} + \frac{1}{2}\arccos\left(\frac{1}{3}\right)\right)$.
16h
answered Could someone explain me the task?
22h
answered Values of $a$ for which $ f(x)=8 a x-a \sin6x -7x - \sin 5x $ increases
23h
comment a linear differential equation with periodic coefficients
Let $a(x)\equiv1$, $b(x)\equiv0$.
23h
answered Does $\frac{nx}{1+n \sin(x)}$ converge uniformly on $[a,\pi/2]$ for all $a \in (0,\pi/2]$?
1d
revised Difficult Coordinate Geometry and Calculus Question
added 137 characters in body
1d
answered Difficult Coordinate Geometry and Calculus Question
2d
comment What do $a_0$ ,$a_m$ and $b_m$ terms mean in the Fourier series formula?
If $\omega$ is a constant then the Fourier expansion of your combined signal is just $$x(t)=2\sin(\omega t)+\sin(4\omega t)+\cos(\omega t)\ .$$ The whole machinery is only needed when the signal is just an old periodic function, and is not already given as a superposition of specific harmonics.
2d
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2d
comment Probability in a Restaurant
What is the definition of a "revolving restaurant" and "different seatings" in such a restaurant?
2d
comment What do $a_0$ ,$a_m$ and $b_m$ terms mean in the Fourier series formula?
The constant term ${a_0\over2}$ in the Fourier expansion of a periodic function $f$ is the average of $f$ over one period.
2d
comment find all continuous functions $f:\mathbb{R}^n \rightarrow \mathbb{R}$ satisfying $f(x+y)+f(x-y)=2f(x)+2f(y)$ for all $x,y \in \mathbb{R}^n$
@John: I don't know yet, or I would have posted it as a solution.
May
25
comment find all continuous functions $f:\mathbb{R}^n \rightarrow \mathbb{R}$ satisfying $f(x+y)+f(x-y)=2f(x)+2f(y)$ for all $x,y \in \mathbb{R}^n$
If $(x,y)\mapsto B(x,y)$ is bilinear then $f(x):=B(x,x)$ satisfies the given functional equation.
May
24
revised Minimum number of moves required to invert a triangular array of coins?
added 29 characters in body
May
24
answered What is real $R$ so that every subset of Euclidean space with diameter one is inside a ball of radius $R$?
May
24
revised Minimum number of moves required to invert a triangular array of coins?
added 132 characters in body
May
24
answered Minimum number of moves required to invert a triangular array of coins?
May
24
revised Minimum number of moves required to invert a triangular array of coins?
added 1 character in body; edited title
May
24
comment Most general linear transformation which leaves the origin fixed and preserves all distances?
The phrase "is either a rotation or a rotation followed by reflexion in the real axis" (taken from Ahlfors) is not utterly wrong, but misleading. It's like saying that a man born in New York is either born in the USA or in China.