Matthew is part of todays reading 1-25. I found this link helpful in relation to Luke. Let me know your thoughts.
Two things may be noted by way of conclusion. First, many rabbinic objections to the messiahship of Jesus are based on his genealogy. The argument goes, “Since Jesus was not a descendant of David through his father, he cannot be Messiah and King.” But the Messiah was supposed to be different. As early as Genesis 3:15, it was proposed that the Messiah would be reckoned after the “seed of the woman,” although this went contrary to the biblical norm. The necessity for this exception to the rule became apparent when Isaiah 7:14 prophesied that the Messiah would be born of a virgin: “Therefore the Lord himself will give you a sign: Behold, a virgin will be with child and bear a son, and she will call his name Immanuel.” Whereas all others receive their humanity from both father and mother, the Messiah would receive his humanity entirely from his mother. Whereas Jewish nationality and tribal identity were normally determined by the father, with the Messiah it would be different. Since he was to have no human father, his nationality and his tribal identity would come entirely from his mother. True, this is contrary to the norm, but so is a virgin birth. With the Messiah, things would be different.
In addition, these genealogies present a fourfold portrait of the messianic person through four titles. In Matthew 1:1 he is called the Son of David and the Son of Abraham. In Luke 3:38 he is called the Son of Adam and the Son of God. As the Son of David, it means that Jesus is king. As the Son of Abraham, it means that Jesus is a Jew. As the Son of Adam, it means that Jesus is a man. As the Son of God, it means that Jesus is God. This fourfold portrait of the messianic person as presented by the genealogies is that of the Jewish God-Man King. Could the Messiah be anyone less?