canvas-raycasting | Canvas Raycasting Experiment | Canvas library

The way that you're mapping (or not, as the case may be) texture coordinates isn't working as intended.

I am looking for the Maths used to produce pseudo 3d effect using 2D raycasting

The Wikipedia Entry for Texture Mapping has a nice section with the specific maths of how Doom performs texture mapping. From the entry:

The Doom engine restricted the world to vertical walls and horizontal floors/ceilings, with a camera that could only rotate about the vertical axis. This meant the walls would be a constant depth coordinate along a vertical line and the floors/ceilings would have a constant depth along a horizontal line. A fast affine mapping could be used along those lines because it would be correct.

A "fast affine mapping" is just a simple 2D interpolation of texture coordinates, and would be an appropriate operation for what you're attempting. A limitation of the Doom engine was also that

Doom renders vertical and horizontal spans with affine texture mapping, and is therefore unable to draw ramped floors or slanted walls.

It doesn't appear that your logic contains any code for transforming coordinates between various coordinate spaces. You'll need to apply transforms between a given raytraced coordinate and texture coordinate spaces in the very least. This typically involves matrix math and is very common and can also be referred to as Projection, as in projecting points from one space/surface to another. With affine transformations you can avoid using matrices in favor of linear interpolation.

The coordinate equation for this adapted to your variables (see above) might look like the following: