Correct UV mapping of sky hemispherical texture

How do you correctly map a sky hemisphere, using an equatorially adjusted fisheye image, of which there are many examples on the net.
I would post the URLs, but I think it isn’t allowed on this forum for some reason.
I know how to map a standard HDRI fisheye image on to a hemispherical mesh in Blender, but some sky textures are stretched-out horizontally.
They are not cylindrical mappings because they are supposedly for hemispheres.

If you google search for: Skybox Textures (4096x1024), you will come across a page full of examples.