I have experience with image processing, but I am fairly new to GIMP. I was experimenting with combining layers that have transparency, and the pixel values that GIMP computes do not agree with the equation I've seen posted on GIMP and photoshop web sites.
Here's a specific example. The math here applies to a single pixel, but for convenience I'll assume that I have images with the same pixel value everywhere. Start with a 4-band image, where the RGB values are all 128, and the alpha layer is all 255, or as a fraction 1.0. Use that as your base layer. Now put on top of that another layer that has RGB values of 0 and an alpha value of 191, or as a fraction, 191/255 = 0.749. When those layers get combined in GIMP, I thought it was done mathematically using the following equation: