Recent content by FranzS

It was a backward explanation to me, so to speak. In @fresh_42 specific example it was clear that the power series diverges for ##x \geq 1##. Sorry

This is already a very good explanation to me, thank you

By the way, I have clear in mind the "circle of convergence" in the complex plane, I was just wondering if there were some other sort of intuitive explanation.

Thanks for your replies. Actually, using a classic specific example, what I meant is: how does a real function like... $$ f(x)=\frac{1}{1+x^2} $$ ... have a MacLaurin series ##m(x), \ x \in \mathbb{R}## with finite radius of convergence when it has no real singularities? Why do complex...

Hello, I've always been fascinated by the fact that even strictly-complex singularities determine the radius of convergence of the (real) Taylor series of a (real) function that doesn't have any singularities in ##\mathbb{R}##. Can anyone provide an intuitive explanation besides the rigorous...

Justification for believing that ##N_c \approx 10^{10}##: a more proper (exact?) estimate of the possible combinations for race categories ##N_r## would be... $$ N_r = \frac{ 12! } { 4! \times 4! \times 4! } = 34 \ 650 $$ ... because all steps A (see post above) will generate a sequence...

@.Scott thanks a lot for chiming in. I'm still studying this "problem" and I plan to post again here when I have relevant results. Anyway, after running some simulations it became clear that the possible configurations of the racers during a race day don't have the same probability. Instead...

How could I not see the direct substitution into the first equation... It seems like I really wanted to re-derive that one as well... My bad. Thanks for pointing it out.

Hi PF, a motion with constant jerk ##j##, i.e. with a constant rate of change of the acceleration with respect to time, should be described by the following equations (hope the variable names are self-explanatory): $$ \begin{cases} a = a_0 + j \ t \\ v = v_0 + a_0 \ t + \frac{1}{2} \ j \ t^2...

Thanks for your reply. The more I think about it, the more I'm convinced that my intuition was completely wrong.

Thanks for offering this point of view. In this case, not knowing ##m(t_0) = m_0##, it makes no sense to use ##m(t \gg t_0) \approx \Delta m(t \gg t_0)## as an estimate for the value at a certain point, because I would conclude that ##m_0 =0## and that's useless.

Hello, do you ever get the feeling that you cannot grasp an apparently easy concept? Like setting up the problem, writing down some equations and not knowing how to go on? Well, I'm in that situation right now. So, I would like to estimate the mass of certain objects by knowing only and...

For the Riemann hypothesis, check out all the videos by YouTube channel "zetamath". Best explanation I could find! Hope he resume the series. For special & general relativity, as well as for other physics-related topics, I recently discovered "Floathead physics", again on YouTube. He really...

Thanks for your answer. As Europeans, we look at EN / ISO standards, but either way we have no reference to any standards in our drawings.

Thanks for suggesting such an example. I'll have to re-read it more carefully because it's not completely clear to me yet, but I guess that's not how the PC game is programmed, as the racers selection seems totally random: even after many races (100+) it often occurs that a particular racer...