The Jewish levirate law states that when a man dies childless his widow - "shall not marry to another; but his brother shall take her, and raise up seed for his brother" (Deuteronomy 25:5). The child of the second marriage is legally the child of the first (Deuteronomy 25:6). Heli died childless. His widow became the wife of his brother Jacob, and Joseph was the offspring of the marriage. Naturally the son of Jacob, but legally the son of Heli. It is likely that Matthew gives the natural descendant and Luke the legal.

6-13-2017 WHY FOUR GOSPELS? It's because the savior was prophesied as a servant, a king, a man, and the son of God. Each gospel treats one of these four aspects. Matthew is the story of a king. The genealogy in Matthew is the royal line, in ascending order because a king traces his ascent to the throne. It is in Matthew that we are told of wise men bringing gifts of gold, frankincense, and myrrh: the traditional gifts to a king. It is in Matthew that another king tries to murder the infant Jesus to protect his own status. It is in Matthew that Jesus declares most of the new, stricter interpretations of the law of Moses, acting on his kingly authority. In Matthew we see the pageantry of an angel rolling the stone away from the tomb and sitting upon it. The other gospels just say the tomb was open. Mark is the story of a servant. It begins, with only a slight preamble, where Jesus's ministry begins. Very little of what Jesus said is recorded, since a servant's opinions and pronouncements are important only insofar as they come from his master. His last words are not recorded, he just "cried with a loud voice." Mark is a short, terse record of where Jesus went and what he did. There is no genealogy because a servant has none.Luke is the story of a man. As such it has a man's genealogy, recorded in descending order because a man traces his descent from an ancestor. The genealogy in Luke is the legal line, beginning with "as was supposed", which is a legal term meaning "determined by law". The genealogy in Matthew is the kingly line, recorded in ascending order because a king traces his ascent to the throne. The genealogy in Luke says so-and-so "son of" so-and-so, and some of the names were in fact adopted sons. But in Matthew it says so-and-so "begat" so-and-so, a purely human genealogy. Mark has no genealogy because a servant has none. John has a very short genealogy: he is the son of God. His last words on the cross, "It is finished", recall his first recorded words, "Wist ye not that I must be about my father's business?"