MWresearch

I guess I just don't see how those two formulas prove anything, to me they just seem like assumptions without any explanation.

I am interested in the process and a specific example behind deriving that gamma(x)*gamma(1-x)=pi*csc(pix). The proof or derivation doesn't seem to exist anywhere online.

Mutiplying by what imaatfal said almost did it in a way, but I ended up only getting the positive side and it was still reflected. And with john, something doesn't add up. I remember from statistics that we used something like sqrt(x^2) for equations dealing with variance and standard deviation specifically to avoid the discontinuity caused by the vertex of |x| at x=0 or wherever the vertex happens to be. Maybe it's something else I'm thinking of?

John: That modular notation does look like an interesting tool that I never considered using before, but I don't think modular-forced equations will differentiate and integrate nicely nor have much use in identities, neither will absolute values. I was hoping for something more traditional and continuous, more like sqrt(x^2) instead of |x|. Imaatfal: Using internet explorer and okay. Yeah I don't think it's purely periodic either, hence the phrase "semi-periodic." Only the discontinuities on the negative side of gamma(x) are periodic and I don't know what that's called, but that phenomena occurs in other equations involving gamma, exponents and trigonometry. Look at tan(x). The same translational pattern occurs to the left and to the right. I want to do that with gamma(x), I want the pattern on the negative part to continue to the positive side of the domain unreflected.

This site is so glitched I can barely even post. In fact, mostly I can't post, I have to refresh the page 3 times to make a single post. I definitely can't post that link. You'll just have to do the exhausting work of typing in a url and equation to see for yourself.

Use wolframalpha, type gamma(-x^2) and don't restrict the domain. You'll get something that looks kind of like cosecant.

Suppose I have a function that has some periodic properties related to discontinuities to the left of x=0 and is mostly monotonic or just a continuous to the right of x=0, like for instance y=gamma(x). How do I make such a function and other special functions always periodic over all the domain without reflection symmetry? If I do gamma(-x^2) the function is periodic over the entire domain, but instead of continuing the periodic property from x=-infinity to x=infinity, the function is reflected over the y axis. I want it to be more rotationally symmetric like tan(x).

Yes, thank you.

To me it sounds like he is making a snide remark by saying there's a delay because someone's arm gets ripped off. In either case, the lack of an answer doesn't excuse purposely adding clearly irrelevant convolutions. Obviously the charge of a black hole isn't remotely related to this problem.

Oh, that is my bad then. Somehow I got continuous curves involving the flooring function when I was looking at weird integrals for functions involving the lambert w function and the gamma function and so I assumed that the "picking between numbers" operation applied equally to decimals. I also just meant monotonic because I was only looking at the first quadrant of x^2.

Saying there's a delay because the arm gets torn off isn't the same as a delay due to time dilation which makes it not what I'm looking for. Even though mathematically you could technically have infinite time dilation at the relative boundary of the black hole which would in practice be the same as never having an arm since in either scenario you wouldn't be able to feel anything, I am specifically talking about above the event horizon, not at or inside it.

I don't care about the exact amount of time dilation, as I said I only wanted a general answer. Does it get delayed due to time dilation, yes or no? That's it, that's all you need to think about and yet you managed to ruin that simple question and turn it into an entire convoluted section of nothing but babble. I specifically specified that I was neglecting harmful effects of tidal forces and harmful effects of force due gravity against what they would be hovering on (which would answer your orbital question anyway) that would harm the person, those are the parameters, a person or a structure resembling person with the ability to withstand up to gravitational force near the surface of a black hole to allow an electrical signal to pass through it from end to end with the focus solely on the general amount of time it would take for the signal to be perceived through the sense of feeling after observing it optically. Would there generally be an increase in the amount of time it would take to feel something? Yes or no? That's it.

I just find it very odd that I would have to break a completely continuous, smooth, monotonic curve into these separate parts that aren't even graphically visible at the points of the derivative or ceiling function. If I had y=x^2, but replaced x with "floor(x)," well the lowest integer between 1 and 1 is 1, and the lowest integer between 2 and 2 is 2 and so on and it should be a continuous curve, yet I still have to break down the simple integral of x^2 into parts at locations that I can't even directly see?

Except you obviously didn't read the first post because then you'd see how nothing you said actually matters for this thread There is some amount of time dilation regardless of the black hole's mass There is some amount of time dilation regardless of the black hole's charge There is some amount of time dilation regardless of the black hole's spin There is some amount of time dilation regardless of whether or an object is falling or orbiting You stated you had no answer and then flip flopped after convoluting the thread and purposely ignoring the parameters I set, making your posts strictly off topic and against forum rules. Mordred indirectly brought up a good point that was actually helpful in simplifying the problem which is the question of whether or not the hand and the brain are in the same frame. Since the signal needs to travel distance over time to get to the brain from the hand, there's a pretty fair chance that they aren't, which would mean that there would be an extended delay in the amount of time it takes for someone to perceive the touching of an object through feeling.

So...it doesn't have a derivative while nested inside another function that produces a continuous curve? Or.... Do I reuse it in such a way that it is its own derivative or integral? Like d(floor(x)^2)/dx = 2(floor(x))?

The delay is extended, that's it, that's all I was looking for. Obviously, I was in no way looking for answers involving someone's arm getting ripped off (which I specified at the start) and obviously saying there's a natural delay has no intrinsic connection to time dilation whatsoever. All of these issues could have been solved simply by slowing down and taking the time to accurately read what I said. The answer is not "it depends," this is not a series of multiple scenarios, this is one very very specific scenario. You originally stated you had no answer after posting material which did not follow the parameters I set, then you said the answer was the violations of the parameters I set, and now you're saying it depends. If you don't know the answer, then please don't unnecessarily convolute my threads.

It's still wildly beside the point, still copout answers because the focus obviously isn't the natural inertial delay they already have, its any extra delay they might have due to time dilation.

What?

So kappa can go from 0 to infinity, but what about like...the angle? I feel like when there's curvature, somehow the angle matters because when I look at the Lorentz transformation the rotation doesn't happen past a certain 45 degree line.

I wasn't looking for a calculation, just a general answer. I don't care what non-zero and non negative length you use. The person could be 100000000000 lightyears large for all I care.

Well it doesn't necessarily have to be those isolated functions, I was thinking more for the chain rule, like if the flooring function was nested inside something else that ultimately produced a continuous curve.

You're not being specific enough for me to understand how your point applies. Could you apply what you're saying to exact elements of the proposed scenario?

So, the reason the black hole mass change due to virtual particles isn't symmetric is because black holes don't gain mass whenever a member of a virtual pair doesn't escape, they only lose mass when one does?

To be honest Strange that's just a copout answer, because electrons and photons and other signals can still travel outward from a black hole so long as they were never observed crossing they event horizon and already mentioned we should neglect the damage a person would suffer at the start.

But that's what I mean, would time dilation actually create a delay in the nerve signals?