Welding of 4340 is carried out using the same material, i.e. 4340, the pre and post heat however is a must due to the high carbon content of the material.
Minimum pre-heat is 320'C (or 600'F), maintain interpass temperature at this minimum, (ms start temp is approx 580'F).
Post weld heat treatment is 550'C (1000'F)
ESAB make a decent electrode for this use ATOMARC E4340
Hope this helps.
Mel