A.T. Robertson Commentary Luke 20:42

"For David himself saith in the book of Psalms, The Lord said unto my Lord, Sit thou on my right hand," — Luke 20:42 (ASV)

For David himself (αυτος γαρ Δαυειδ). This language of Jesus clearly means that he treats David as the author of Ps 110. The inspiration of this Psalm is expressly stated in Mr 12:36; Matthew 22:43 (which see) and the Messianic character of the Psalm in all three Synoptics who all quote the LXX practically alike. Modern criticism that denies the Davidic authorship of this Psalm has to say either that Jesus was ignorant of the fact about it or that he declined to disturb the current acceptation of the Davidic authorship. Certainly modern scholars are not agreed on the authorship of Ps 110. Meanwhile one can certainly be excused for accepting the natural implication of the words of Jesus here, "David himself."

In the book of the Psalms (εν βιβλω Ψαλμων). Compare 3:4 "in the book of the words of Isaiah the prophet."