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Jun
14
accepted Can any analytic function be represented as a sum of a Newton series and a periodic function?
Jun
14
asked Can any analytic function be represented as a sum of a Newton series and a periodic function?
Jun
14
revised If two functions are equal to their Newton series, is their composition also equal to its Newton series?
added 9 characters in body
Jun
14
comment Is composition of analytic functions itself analytic?
What do u think about this? math.stackexchange.com/questions/834257/…
Jun
14
asked If two functions are equal to their Newton series, is their composition also equal to its Newton series?
Jun
14
comment Best mathematical object to describe speed
@dmckee Here is asmall table of what do I mean (assuming $t_1$ is always zero and the cause is in x=0, t=0): $$\left( \begin{array}{cccc} x_1 & x_2 & t_2 & v \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 1 & 1 \\ 0 & -1 & 1 & -1 \\ 0 & 1 & 0 & \omega \\ 0 & 1 & -1 & \omega +1 \\ 1 & 1 & -1 & 2 \omega \\ 2 & 1 & -1 & 2 \omega +1 \\ 0 & 1 & -\omega & 2 \omega \\ 0 & \omega & 1 & \omega \\ 0 & -1 & 0 & -\omega \\ \end{array} \right)$$
Jun
14
comment Best mathematical object to describe speed
@dmckee your formula does not take into account what is cause and what is effect. You got -1 even for the case where the explosion happened before the shot as if the explosion were the cause.
Jun
14
comment Best mathematical object to describe speed
@dmckee For example, if the shot and the explosion happened simultaniously, the speed depends on where is the shot. If the shot is in 0, then the speed is $\infty$, if in 1, then the speed is $-\infty$.
Jun
14
comment Best mathematical object to describe speed
@dmckee it depends on what is the cause. We can assume the cause (cannon shot) to happen at t=0 x=0 and look where and when the explosion happened.
Jun
14
comment Best mathematical object to describe speed
@dmckee because it reached the destination before the origin. The target exploded before we fired. What's the projectile's speed?
Jun
14
revised Best mathematical object to describe speed
added 56 characters in body
Jun
14
asked Best mathematical object to describe speed
Jun
14
comment Is composition of analytic functions itself analytic?
@Giuseppe Negro prove
Jun
14
comment Is composition of analytic functions itself analytic?
This requires first the proof that any differentiable complex function is analytic, which I think is a non-trivial theorem. Anyway, what about real analysis? Can this be proven without complex numbers?
Jun
14
comment Is composition of analytic functions itself analytic?
@Giuseppe Negro and what? these problems do not make it non-analytic and non-holomorphic.
Jun
14
revised No extension to complex numbers?
edited body
Jun
14
asked Is composition of analytic functions itself analytic?
Jun
14
answered No extension to complex numbers?
Jun
13
comment What is $\tan50^\circ$
@David H haha, very funny
Jun
13
comment What is $\tan50^\circ$
1.19175 is not the exact value.