Can anyone help me to find what function produces a plot like this one? Also, if possible, how could I plot it using LaTeX in a grid? I guess it is some kind of composite functions but I tried simple guesses and they do not work. Ideas?
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This curve looks to (be at least very close to) have this equation:
$$y=-\ln(x)-\sin(x)$$
adding to a logarithmic "carrier" (taken with a minus sign) a regular sinusoidal pulsation.
In fact, the pulsation of the sine wave should be slightly different. Indeed, by taking
$$y=-\ln(x)-\sin(0.9*x)$$
one gets the exact number of maxima in the [0,160] range.
(I have checked the plot).
Remark: at first, instead of the $\log$ function, I had taken a fractional power law $y=-x^{1/2}$ for the "carrier" but the behavior in the vicinity of $0$ wasn't satisfying...
Jean Marie
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Maybe the it is $\sin(\frac{3x}{\pi})$ in place of $0.9$, but we cannot know for sure unless we have exact values ? Anyway it seems to fit quite nicely indeed. – zwim Nov 08 '21 at 19:44
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Indeed, I have thought to this coefficient $3/\pi$ ! – Jean Marie Nov 08 '21 at 20:15