You can just about do it for that shape, but it's not very flexible. This is in Illustrator: Photoshop's 3D tools (which I don't know well) are much more sophisticated but based on similar principles.
1- Prepare a flat image as if it was going to be wallpaper on the flat wall. Drag it into the Symbols panel (
Window > Symbols)
2- Make a vertical line. Revolve (
Effects > 3D > Revolve) it 180 degrees with an offset, forming a curved wall.
3- Map Art the wallpaper onto the appropriate face of the wall.
Changing the shape of the wall from a circle to something longer and thinner isn't easy in Illustrator (might be easier in PS). One way is to simply expand the effect, then scale the thing so it's thinner. If you're doing this, make a note of the numeric scaling value, then create a variant of your wallpaper fattened by 1 over that value as a decimal so you end up with non-distorted wallpaper (e.g. if you're going to make it 80% width, 1 / 0.8 = 1.25 so stretch the wallpaper 125% width).
Here's a low-res example with 800% / 12.5% scaling:
No infinity, but up the perspective and increase the scaling until the end point gets close to being less than 1px or one dot on a printed page, then just let it disappear.