What mathematical function could be used to simulate this sound effect?
I guess you want to synthesize that sound, i.e. create a synthetic signal to be as close as possible to the original sound. Potentially, you can do this by creating a superposition of sine waves with varying amplitudes and phases. So you have to know the parameters for those sine functions.
From what I can see and hear, the sound has two signals, which are very similar (both visually and to ear). Moreover, if you look at the frequency spectrum, you will see, that they are quite similar as well. However, the spectrum seems quite populated with different frequencies, which will make it difficult to reproduce as a synthetic function. At least if using only the provided original sound file.
Here is the spectrum plot:

And here is a python code to make those observations. (The file with sound is downloaded to the folder of the python script.)
import matplotlib.pyplot as plt
import soundfile as sf
import sounddevice as sd

# get file
filename = &quot;SoundEffect.wav&quot;
x, f = sf.read(filename)
x1 = x[:,0]     # the first signal
x2 = x[:,1]     # the second signal

# play and show the original sound in time domain
sd.play(x, f)
status = sd.wait()
plt.plot(x)
plt.show()

# play the first signal
sd.play(x1, f)
status = sd.wait()
# play the second signal
sd.play(x2, f)
status = sd.wait()

# show the signals in frequency domain
plt.magnitude_spectrum(x1, Fs = f)
plt.magnitude_spectrum(x2, Fs = f)
plt.show()

Bear in mind, I am not familiar with how sound effects are done. Most probably, this sound effect is a more simple superposition of certain signal shapes. However, unless they are already known, it is hard to &quot;reverse-engineer&quot; them from the sampled version of the signal.