What kind of curve is this? It seems like some kind of Sine curve with another higher-order term in front, but I don't know enough about fitting to find a good fit. Here's the Mathematica code to plot it:
Monitor[ListPlot[Table[Product[N[Abs[1/(1 - Prime[x]^(-(1/2 + 3*I)))]], {x, 1, y}], {y, 1, 1000}]], y]
by the way, this takes a long time to run, so you might want to run it to 500 instead of 1000.
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here's another pic of 1->200
bump
What kind of answer are you look to get on this?
for someone who knows statistics better than I to suggest a model for me to try fitting. It looks a lot like a Sine function but nothing I've tried works.
you've got the function that makes it, but you want to fit a different curve to it?
Just eyeing it, it looks a bit like y = x^2 * (sin x)^2 or e^x (sin x)^2 or e^x (sin x) ^ 4
or some combination thereof.
I cant remember a lot but with fourier analysis you can fit any linear combination of sines and cosines to that.
Or if you know the basic functions () you can just use linear regression to find the constants.
had no idea you could do that now.
thanks.
try taking the derivative a bunch of times see what comes out.
here's the fourier transform. I think this means nothing will fit to it.
what do you mean?
the graph function on google.
thats just a frequency distribution.
fourier transforms can fit literally anything.
actually I don't know
this.
find the base functions if you can, then linear regression, and you're done
on second thought that looks more complicated than a simple sign. almost like the output from a nonlinear ODE.
Yes, but not cleanly. I'm looking for a meaningful result, not a 100-term mess
This is the path of rotation for an egg that grows in size when it rotates.
sorry, I got nothin for you.
dont know mathematica well
works in 3D too
interesting conjecture, elaborate?
no. egg does not have radius=0 as it rotates.
sweet
If anyone wants to know what this really is, it's the convergence of the infinite Euler product of the Riemann Zeta function at [math]s = 1/2 + 3i [/math]. The Zeta function built in to Mathematica calculates it as an infinite sum, but it can also be done using primes in the denominator, and I was curious to see how it converged.
Here's the plot of Abs[Zeta[1/2 + 7i]] starting to converge to the line
physics background and hated complex variables (fuck it all beyond eulers formula) so know nothing of riemann function.
Was thinking it was y= x^2 * sin (x^2) before you posted, as frequencies seems to increase with x....
anyway, good luck
Yeah I'm an ee student so I don't really know what I'm doing either. I really don't see how could ever converge to that line. If Terrence Tao can't figure it out then I probably shouldn't bother, but it's a fun way to kill time.
I think I'll interpolate the table and try to make a Fourier series out of it
>could ever converge to that line.
there's a sine in there somewhere...
>radius not 0
Not measuring the radius measuring the height of the tip relative to the ground.
ya... i suppose.
I think that would look more like a leapfrog function, though. Someone with more energy could probably write the function you have in mind for a circle, and they'd look very similar.
fuck im dumb
not sure what I was thinking with
anyway its called a cycloid egg... what you're thinking of
been way too long, and im tired.
The Virgin little bump
The Chad large mound
How about the Fourier transform of the Fourier transform of ?
Sin wave scaled in height exponentially and scaled in width by an exponential modulated by a sin wave
Instead of settling on something arbitrary like -1/2 - 3*i you should ask yourself what's going on at a general complex number z. If you write what you've got here as a function [math]\mathbb{C}\times\mathbb{N}\to\mathbb{R}[/math] and plot it over the complex plane at different integer values you'll see that what's really going on is that you're taking the z-coordinate of a little surfer as they ride a series of crazy waves.
Is there some continuous, closed-form parameterization of their trajectory? Maybe, but I don't see any reason for there to be.
How is possible that there is no other closed form description of it? I picked 1/2 and 3 because I was mostly interested in the properties of the primes and I wanted to focus on one little spot on that plane.
>How is possible that there is no other closed form description of it?
For the same reason that it's possible that huge classes of functions have no closed form antiderivative.
It wouldn't have to be closed form necessarily, but it obviously must have some sort of sine factor and it's frustrating that it's unknown.
It's a Bitcoin curve, obviously.
>but it obviously must have some sort of sine factor
Be wary of trusting your sense of what is obvious is mathematics.
kek retard