Adobe has published some of the blending modes as PDF specification. Check this : https://www.adobe.com/content/dam/acom/en/devnet/pdf/pdf_reference_archive/blend_modes.pdf
All calculation formulas seem to be absent in Photoshop's user quides. I guess you need an in-group contact to get exact blending equations or you must reverse engineer Adobe's program code. That is probably forbidden in the usage license.
Nothing quarantees Photoshop uses PDF blending modes exactly. Color burn seems to test in the beginning if the backdrop has R,G or B =255 and in that case the result is 255. If the backdrop has 0...254, then the PDF calculation seems to be used in Photoshop, too.
BTW. This has been wondered a long time. You are not the first one. See this older case. I copied the guessed explanation from there after trying it:
Why is color burn not affecting a white channel?
In color dodge there seems to be in the beginning a test if there's R, G or B =0 in the backdrop. In that case the result is 0, otherwise It's calculated with PDF formula