Question: From where does the story of Jesus' Transfiguration come? Is there a story like this one with regard to any of the other prophets?
AP: The "Transfiguration of Jesus" is a tradition that began with Mark. We have no Christian antecedent. And there is nothing strictly Jewish about it. Mark wanted us to understand that Jesus is the "adopted son of God" after his baptism and that, according to Roman adoption laws, he is divine (in some sense of the word).
What we do have in the Greco-Roman world are the history of the gods that walked incognito among men on the earth, testing mortals and if the result was positive, they would reward them and appear to them in all their glory. The story was, we could say, floating around in the air. But the background of the divine confirmation of Jesus as Messiah, by Moses and Elijah, at the Transfiguration is already the byproduct of Christian theology. It is not historical.
TWH: The data we have concerning Jesus' transfiguration comes to us from eyewitnesses. Peter, James, and John were instructed to not tell anyone about the amazing event until later. Two of them–James and John–were so blown away at what they saw that they sought to procure the seats of honor in Jesus' kingdom. Peter mentions it in a letter before he is martyred (2 Peter). They clearly shared the news about Jesus being transfigured following the resurrection. The event is historical. And the event has a connection to God's dealings with the descendants of Abraham as well. Don't forget about Moses' face shining, which Paul references in 2 Corinthians (see chs. 3–4). Moses, we remember, had to cover his face. Jesus does not. That's very interesting. I would see that as a better connection to what happens to Jesus on the mount than any reference to Greek gods in ancient literature.
Question: How did the Persian religion influence Judaism and Christianity?
AP: I have published two books, which I edited and contributed to, that feature an analysis of this topic. One is Orígenes del cristianismo, originally published by El Alemendro (Córdoba) in 1992. The other is Biblia y Helenismo. La influencia del pensamiento griego en la formación del cristianismo, also published by El Alemendro in 2006. There is a chapter by Anders Hultgard that deals specifically with the question at hand.
Briefly let me say this. The influence really falls in the area of a dualistic conception of the divine. For example, it influenced the way Judaism and Christianity thought about angels and demons; the spiritual man and the physical man; the existence of divine retribution; the world below, with its sorrows and glories; and final judgment. Keep in mind, though, the Jewish worldview received a lot of this from the Greek world.