Factorials as Multiplicative Integrals

In which we try to figure out what what’s going on with double-factorials. This was formerly part of the previous post about (n)-spheres, but I started adding things to it and decided to split them up. It is not necessary to read the original previous post first, but it is sort of a sequel, since it’s the direction my investigation has gone. Both articles are essentially unwieldy dumps for notes and calculations that I’ve done and wanted a record of, but maybe they’ll be useful as a survey if anyone else