This page here describes that the focal length does not result in perspective distortion:
"Yes, there are optical distortions in lenses, but those have nothing to do with the focal length."
while this page here describes if you increase the focal length and camera distance to infinity then it results in orthographic projection(affecting the perspective):
Increasing the focal length and distance of the camera to infinity in a perspective projection results in an orthographic projection.
So, what is the mathematical relationship between focal length, camera distance and the perspective projection.
P.S: If changing the focal length doesn't affect the perspective of the image, what affects the perspective distortion of the image?(please do show the fact mathematically)