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Heli is not mentioned in the genealogy of Jesus from David via David's son Solomon in the Gospel of Matthew, the only other canonical gospel to include a genealogy, although there is a similarly named "Matthan" four generations before Jesus.
Since Joseph cannot be both "begotten of Jacob", descended from Solomon (according to Matthew 1), and also "of Heli", descended from another of David's sons, Nathan (according to Luke 3) various explanations have been proposed for the Luke genealogy actually to be that of Mary. The view is relatively late; advocates of this view include John of Damascus (8th century), Annius (15th century), Luther, Bengel and Lightfoot. Harry A. Ironside (1930) considered that it was simply preference to drop women's names out of the genealogy, hence Joseph was son in law of Heli.
Prior to the explanation above, the explanation of Sextus Julius Africanus that there had been a levirate marriage and that Joseph's grandfather Mattan (descendant of Solomon) had had a wife called "Esther" (not recorded in the Bible) with whom he fathered Jacob (Joseph's father), but Matthan died and Esther married Heli's father Melchi (descendant of Nathan). Then when Heli died childless (again not recorded in the Bible) Joseph's father Jacob took Heli's wife to raise up children for Heli and left Joseph adopted in Heli's widow's house.
Another possibility is that since both Heli and Jacob have a similar name listed as their father (Matthan in Matthew, Matthat in Luke), a discrepancy that can easily be accounted for by error, that the names Heli and Jacob refer to the same person. Matthew relied heavily on fitting existing prophecy to the narrative; in the Old Testament, Jacob (the last of the biblical patriarchs) also had a son named Joseph. This explanation fits for Heli/Jacob himself, but not for the earlier genealogies.
If the situation is reversed, Matthew's genealogy is that of Mary, Luke's of Joseph, then there is a problem with the curse on the Solomonic line, dating from the time of Jechoniah where Jeremiah pronounced that no descendant of Jeconiah would again sit on the throne of Israel. Although Israel had at least one Solomonic descendant, Zerubbabel as governor under the Persians, Zerubbabel never was crowned king.