Boyd’s Bible Dictionary:

(birth record). In Hebrew, “book of generations” (Gen. 5; 10; 1 Chron. 1-8; 9:1; Matt. 1:1-17; Luke 3:23-38).

Concise Bible Dictionary:

This is given in Matthew 1 and Luke 3. According to the distinctive character of Matthew in which Christ is emphatically the Messiah and Son of David, the genealogy commences with Abraham; whereas in Luke, in which Christ is displayed as the Son of Man, the list is traced up to “Adam who was the son of God.” Both lists are the same from Abraham to David; then they differ until they reach Salathiel and Zorobabel, which names are in both lists; and then they again differ. The list in Luke is much fuller, having from David to Joseph forty-one names, where Matthew has only twenty-six. Names are omitted from Matthew, and this enables the whole to be brought into the three divisions of “fourteen generations.” Ozias is placed as the son of Joram, but on consulting 1 Chronicles 3:11-12 (where for Ozias is read Azariah, as also in 2 Kings 14:21), it will be seen that three kings are omitted, Ahaziah, Joash, and Amaziah. Such omissions are found in the genealogies in the Old Testament In 2 Chronicles 22:9 Ahaziah is called the son of Jehoshaphat; whereas he was his grandson; and by comparing the generations in 1 Chronicles 6:3-15 with Ezra 7:1-5 seven names will be found to be omitted in the latter.
It will be noted that in Matthew the word “begat” is used, whereas in Luke it is more indefinite. Jesus was “supposed” or “accounted” to be the son of Joseph, and “Joseph was of Heli” without the word “begat.” Again, it should be noted that by a Jewish law if a man died childless, his brother was to raise up seed to the deceased by his widow, so that a son born thus might be called the legal son of the deceased, whereas he would be the actual or lineal son of his father, the brother of the deceased. The list in Matthew is clearly the royal line; between David and Salathiel twelve kings are given, all of whom are omitted from Luke. Being the royal line it must also be the legal line.
There is more difficulty as to the genealogy in Luke: is it the lineal line of Joseph or Mary? Women are never quoted as forming a line of succession, yet Christ is spoken of as the “seed” of the woman (Gen. 3:15); “come of woman” (Gal. 4:4); “the seed of Abraham” (Heb. 2:16); “the seed of David according to flesh” (Rom. 1:3; 2 Tim. 2:8); “the offspring of David” (Rev. 22:16). And as the Lord was not really the son of Joseph, these scriptures can only be fulfilled through His mother, who must have been a lineal descendant of David and Abraham. It is better therefore to consider that Luke gives the lineal descent of the Lord through Mary. In accordance with the above it will be seen that Matthew in speaking of the birth of the Lord frequently mentions Joseph, seldom Mary; whereas Luke frequently mentions Mary, but seldom Joseph.

Strong’s Dictionary of Greek Words:

from the same as 1075; tracing by generations, i.e. "genealogy"
KJV Usage: