This article is within the scope of WikiProject Numbers, a collaborative effort to improve the coverage of Numbers on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.NumbersWikipedia:WikiProject NumbersTemplate:WikiProject NumbersNumbers articles
I am not a mathematician, and don't know much about hypertranscendentals, but Shannon's 1941 analysis of the differential analyzer (available in his Collected Papers; see p. 507) includes the phrase, "providing the functions f_k are combinations of non-hypertranscendental functions" when discussing the computational power of the D.A. This suggests that the term was in common use by then, though perhaps its definition was not yet formalized.