Codex @codex  0

By Peter Hall.

Publisher: link.springer.com/book/10.1007/978-1-4612-4384-7

Chapter scan: people.eecs.berkeley.edu/~jordan/sail/readings/edgeworth.pdf

Chapter 2, Principles of Edgeworth Expansion, pages 39–81: cumulant/characteristic-function expansions, smoothness conditions and lattice corrections. The publisher identifies the original 1992 copyright; its 2013 electronic publication is not a new edition. The wiki states a stronger smooth-density sufficient setting and derives its first correction explicitly.