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Christ's genealogy per the gospel of Luke is sometimes appropriated to establish his
mother's connection to David, but I don't recommend that route because the
language, the grammar, and the punctuation of Luke 3:23 are much too
controversial.
It's also been suggested that both genealogies are Joseph's. However, in Matthew's
genealogy, Joseph descends from Solomon, whereas Luke's has him descending
from Solomon's brother Nathan.
Solomon and Nathan weren't distant kin. According to 1Chron 3:5 they were
siblings; both born of David & Bathsheba (a.k.a. Bathshua).
I have no clue how it's possible for two siblings to both be somebody's grandfather
when it's more likely that one of them would've been an uncle.
Along with that: there's a serious question about the listings of Shieltiel and
Zerubbabel. In Matthew's genealogy the two men are linked to David via Solomon.
In Luke's genealogy, they're linked to David via Solomon's brother Nathan.
Their respective descendants are different too. Zerubbabel's son is listed as Abihud
in Matthew's genealogy, whereas his son is listed as Rhesa in Luke's.
It's been suggested that Shealtiel and Zerubbabel are common names so we
shouldn't be surprised to find them listed in both genealogies. However, they are
listed as father and son in both genealogies, which we cannot expect reasonable
people to accept as mere coincidence.
Unfortunately, to date there exists no consensus among the experts how best to
resolve the confusion caused by the presence of Shieltiel and Zerubbabel in both
genealogies. Were we scientific in our thinking; we'd have to consider the data
compromised; which is unfortunate because if we disregard Luke's genealogy, then
we pretty much have to disregard Matthew's too.
So the situation with Jesus' genealogies is such that I think it best to go about
establishing his family history from a different angle.
_