Sometimes some of the ancestors mentioned in Luke 3 are included. The genealogies of Matthew and Luke are quite different. To reconcile the difference, Luke 3 is often thought of as the ancestry of Mary, mother of Jesus
Once the canonicity of the gospels of Matthew and Luke was established, the early church fathers had to reconcile the differences between the two gospels. Modern scholarship dismisses the issue by considering the genealogies in Matthew and Luke as inventions conforming to Jewish tradition and having a liturgical and propaganda purpose for the Christians who had to combat skepticism about Jesus.
But the early church fathers were not so willing to dismiss the issue. They were well aware that the listing of ancestors in Matthew 1 and Luke 3 were quite different. Not only were the names different but different numbers of generations were given for roughly the same time period. Various explanations arose such as the fact that the persons named were the same but remembered by different names. But this can only go so far. In Matthew, Joseph is the descendant of King Solomon, but in Luke, Joseph is the descendant of Solomon’s brother Nathan. Levirate marriages were proposed and given as explanations at a couple of points in the genealogies. (For an interesting contemporary discussion about this problem see this blog from Paul Davidson, "What's the deal with Matthew's genealogy?" <https://isthatinthebible.wordpress.com/2014/07/19/whats-the-deal-with-matthews-genealogy/>)
Then the issue of Mary’s Davidic ancestry had to be answered. Mary’s marriage to Joseph who was from the line of David seemed inadequate. Augustine took up the challenge in Contra Faustum Manichaeum. Augustine made three explanations: 1. Jesus placed no emphasis upon his genealogy and urged his disciples to call no man “father” (Matthew 23.9). 2. Jesus was the son of the Father and of his earthly mother Mary who could also be a descendant of David. 3. Joseph, Mary’s husband, was the son of Jacob and adopted son of Heli. Many centuries later, Thomas Aquinas repeated another explanation: “Others … suppose that Matthew gave the forefathers according to the flesh: whereas Luke gave these according to the spirit, that is, righteous men, who are called (Christ's) forefathers by likeness of virtue.”
The easiest way to solve the problem was to separate the genealogies. Assign to Joseph the genealogy recorded in Matthew 1. Assign the genealogy in Luke 3 to Mary. This meant that the significant differences between the two as written did not have to be reconciled.
Medieval clerics and monks would have known the genealogy recorded in Matthew 1.1-17. The long list of names was read or chanted at the celebration of the Nativity of the Blessed Virgin Mary on September 8th. Therefore, the monks would have been familiar with the names. Today one almost never hears the genealogies in Matthew and Luke read. Neither are appointed readings in the Revised Common Lectionary though the Matthew 1 genealogy is still used (as an optional reading) for the feast for the birth of St. Mary on September 8th in the Roman Catholic Church.
Genealogy was of great interest to the nobility and aristocracy of the Middle ages and the Jesse Tree was form of family tree. In addition to the genealogy of Jesus, the Jesse Tree incorporated passages from the Old Testament thought to foretell the coming of a Messiah. The prophesy that forms the basis of a Jesse Tree is the given by the Prophet Isaiah in Isaiah 11.1: “A shoot shall come out from the stock of Jesse, and a branch shall grow out of his roots.” The verse in Latin (Clementine Vulgate) is “et egredietur virga de radice Iesse et flos de radice eius ascendet.” 
The other passage cited is Jeremiah 12.5: "Behold, the days come, saith the Lord, that I will raise unto David a righteous Branch, and a King shall reign and prosper, and shall execute judgment and justice in the earth." In Latin: "ecce dies veniunt ait Dominus et suscitabo David germen iiustum et regnabit rex et sapiens erit et faciet iudicium et iustitiam in terra,"
Given the hereditary requirement for many position in Hebrew society, the ancestry of Jesus was important. This interest in genealogy continued with the nobility and aristocracy of the Middle Ages.
 The Latin Bible used here is Biblia Sacra juxta Vulgatam Clementinam or Clementine Vulgate. There are differences from the Clementine Vulgate edition and the Nova Vulgata that is available at the Vatican website: http://www.vatican.va/archive/bible/nova_vulgata/documents/nova-vulgata_index_lt.html.