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Jul
19
comment Proof or source for this Hurwitz Zeta function identity?
Sorry but where do u see the relation on the wikipedia page?
Jul
19
comment Proof or source for this Hurwitz Zeta function identity?
@Mhenni Benghorbal I do not remember, it was long ago, so I lost the link to the source. I only can say I found it in an article published in the Internet.
Jul
19
comment Proof or source for this Hurwitz Zeta function identity?
@Mhenni Benghorbal this is exactly I am asking for.
Jun
26
comment Is there a formula to quickly express delayed functions in terms of finite differences?
@Did what is inflammatory in unaccepting a wrong answer and accepting a correct one?
Jun
25
comment Is there a formula to quickly express delayed functions in terms of finite differences?
Thanks for the correction, but copying my answer and downvoting it is not a good behavior.
Jun
25
comment Is there a formula to quickly express delayed functions in terms of finite differences?
Can anyone explain the downvote?
Jun
25
comment Is there a formula to quickly express delayed functions in terms of finite differences?
This is wrong, $y(x+2)=\Delta^2 y(x)+2\Delta y(x) +y(x)$ Where is the coefficient in your formula?
Jun
15
comment If two functions are equal to their Newton series, is their composition also equal to its Newton series?
@Giuseppe Negro well, I has been given a counter-example: $f(x)=\sin(\pi \sqrt{x})$, $g(x)=x^2$
Jun
15
comment Were there attempts to build a system of numbers where division by a negative number is greater than division by any positive number?
well I've read that article. It says "A substance with a negative temperature is not colder than absolute zero, but rather it is hotter than infinite temperature." This means that even though it has some properties of negative temperature, its energy level is still greater than that of cold quantities. As such, the sustem with "higher than infinite" temperature can be distinguished by measuring the total energy. This creates well-ordering. So it is exactly what I am talking about: not a circular real line, but a spiral one.
Jun
15
comment Were there attempts to build a system of numbers where division by a negative number is greater than division by any positive number?
I want the tangent of 3/4 pi be greater than the tangent of 1/4 pi. That is the tangent to be monotonously increasing. This is applicable in geometry and in physics when measuring speed of particles. On projective real line they are equal (just as on non-extended real line).
Jun
15
comment Were there attempts to build a system of numbers where division by a negative number is greater than division by any positive number?
The projective real numbers line is not ordered, so the whole point of this quention is ignored.
Jun
15
comment If two functions are equal to their Newton series, is their composition also equal to its Newton series?
@Giuseppe Negro there is no total analogy though. If we allow complex functions, then there is a counter-example, for instance, $g(x)=2\pi i x$, $f(x)=\exp(x)$. That's why I limited the question to real-valued functions.
Jun
15
comment Modified division, hyperreal numbers and transfinite derivatives
No, $\frac{a}{-b}\ne\frac{-a}{b}$
Jun
14
comment Is composition of analytic functions itself analytic?
What do u think about this? math.stackexchange.com/questions/834257/…
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
comment Is composition of analytic functions itself analytic?
@Giuseppe Negro prove