Actually, it goes back to 1931. Abdel-Aty references for that central case (though he misspells Hilferty as Hilfertz): Wilson, Edwin B., and Margaret M. Hilferty. "The distribution of chi-square." Proceedings of the National Academy of Sciences 17.12 (1931): 684. And so does Wikipedia; see the Wilson-Hilferty transformation (same as was pointed out in Abramowitz and Stegun), even in the 2011 version you started with: the Wilson-Hilferty transformation. Too bad the connection wasn't made there. I'll fix it.