According to some sources, the post below that Capitol 797 represents the first professional recording on which Coltrane played is wrong. The Coltrane discography at jazzdisco.org (and indeed, apparently all relevant discographies at this well-respected site) shows Coltrane made his recording debut at the Dinah Washington sessions of September 27, 1949. The credits on the 3-CD set “Complete Dinah Washington on Mercury, Vol. 1”, the CD “John Coltrane Complete Recordings with Dizzy Gillespie”, and many other references perpetuate this idea. The picture is the cover of Mercury EP 1-3207, an original issue 45 containing four of the tunes from this session; the band is not listed.
The John Coltrane Reference by DeVito, Fujioka, Schmaler, and Wild (Lewis Porter, ed.) has a note specifically stating that Coltrane was not present at the Dinah Washington session. (It also notes that the Billy Valentine session typically listed as November 7, 1949, and thus also predating Capitol 797, was probably actually recorded on March 1, 1950; but at least there is general agreement Coltrane was there even if the date is disputed.) The Reference is so well researched and documented that it must be considered definitive. Yet it does not give any indication as to why the error on the discographies may have occurred.
Did Coltrane record or even play with Dinah Washington? It seems clear that Coltrane joined the Gillespie group around September 1949. Dizzy and the gang were appearing around this time on many of the same bills as Dinah Washington. Teddy Stewart, whose band is credited as backing Dinah Washington for the session in question, left the Dizzy Gillespie band around October 1949 to tour with Washington, with whom he may have been involved, according to Lewis Porter's book “John Coltrane.” But as of yet I cannot point to any particular source for the (apparent) misunderstanding over Coltrane's presence at the Washington session. Research on this question will continue, and anyone with relevant knowledge is invited to ring in.