A very incomplete list of some people in Exponential Asymptotics:
George Stokes (1819 – 1903)
John Robinson Airey (1868–1937)
John Heading (1924 - 1991)
Richard Ernst Meyer (1919 – 2008)
Robert Balson Dingle (1926 - 2010)
Frank W. J. Olver (1924 - 2013)
Richard Bruce Paris (1946 - 2022)
Without any order
Michael Berry
John R King
Christopher J Howls
Adri B. Olde Daalhuis
S. Jonathan Chapman
Richard H Tew
John Boyd
Scott McCue
Christopher Lustri
Philippe Trinh
will be updated ...
I would appreciate it if you could suggest further missing names.