Matthew 1:6-11 ‘And David begat Solomon of her that had been the wife of Uriah; and Solomon begat Rehoboam; and Rehoboam begat Abijah; and Abijah begat Asa; and Asa begat Jehoshaphat; and Jehoshaphat begat Joram; and Joram begat Uzziah; and Uzziah begat Jotham; and Jotham begat Ahaz; and Ahaz begat Hezekiah; and Hezekiah begat Manasseh; and Manasseh begat Amon; and Amon begat Josiah; and Josiah begat Jechoniah and his brothers, at the time of the carrying away to Babylon.'
This next section of the genealogy shows the royal line from David to Jechoniah, with omissions (see 1 Chronicles 3). Their lives are described in some detail in the books of Kings and Chronicles. Some think that the omissions of Ahaziah, Joash, and Amaziah arise from the curse placed on the house of Ahab in 1Ki 21:21-24; 1 Kings 21:29, with it being seen as covering three generations until it was purged, for the house of Judah were associated with the house of Ahab at that time by marriage. Ahaziah was the son of Ahab's daughter, and followed in Ahab's ways (2 Kings 8:26-27) and was therefore implicated in the curse. All three kings who are omitted (both good and bad) met a violent end and were slain by conspirators. The kings that are, however, mentioned in the list also make up both good and bad, so that there is no distinction on those grounds. The connection with Ahab seems to be the significant factor.
When we come to the time of Jehoiakim and Jehoiachin the name ‘Yoakim' (Jechoniah) was used in Greek and in LXX for both Jehoiakim and Jehoiachin. ‘And his brothers' may suggest that the former is intended, but Matthew may in fact have intended both kings to be read in here, with the description ‘brothers' indicating ‘relatives' and intended to cover Jehoiakim's different relatives who were associated with the throne over the period (thus including Jehoiachin his son and Zedekiah his brother, who both reigned, the latter at the same time as the former who was then in exile), and thus covering the final complicated situation of kingship over that period of three progressive exiles, with the new Jechoniah then seen as taking up from the old in the third part of the genealogy, for the name(s) ‘Jechoniah' is/are needed in both lists to make up the fourteen, and he would not want to say ‘Jechoniah begat Jechoniah' (i.e. that Jechoniah was Jechoniah's heir). This would explain the mention of ‘his brothers' in this case, for, unlike in the case of Judah, there is no real reason otherwise for mentioning Jehoiakim's ‘brothers'. We should note that here in this middle section of the list there is the clear indication that this is a genealogy depicting heirs to the throne rather than actual direct descent.
Note the mention of ‘the wife of Uriah', and the deliberate non-mention of her name (which differentiates her to some extent from the other three). The non-mention of her name, plus the link with her murdered husband, may suggest here a disapproving reference. Omission of names often indicates disapproval (compare the omission of Simon in Deuteronomy 33 after the sin at Baal-peor). The line was thus to be seen as not whiter than white. And yet she had no doubt sought and found forgiveness, as David also had (Psalms 51). We are reminded by this that the descent includes those who had been involved in deep sin. In the end even David was to be seen as marred, something which the mention of his adulterous wife and the man he murdered emphasises. This was indeed one reason why Jesus had to be born of a virgin. It is doubtful if the fact that Uriah was a Hittite is in mind here, otherwise Matthew would have mentioned the fact. Indeed it seems probable that Uriah was seen as a fully acclimatised proselyte, along with many of David's mighty men, and was also possibly descended from one. But ‘the wife of Uriah' was both the cause of David's partial decline, and the mother of the king who started so promisingly and ended up totally discredited, something which led on to the division of Israel into two parts, and the final decline of both of those parts which resulted finally in the Exile.