Some 15 times in the Word, these are mentioned... the God of Abraham Isaac and Jacob.
why these 3?
One way of answering this question is based on the quote below, about how our world is the "lesson book of the universe".
The first paragraph of the quote discusses this point in connection with Abraham and Isaac, and the second paragraph says that heavenly beings were witnesses of what played out on earth.
The idea of our world as a lesson book is suggested by passages like Job 1:6, Job 42:7, Daniel 7:9-10, Ephesians 3:9-11, and 1 Peter 1:12.
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The sacrifice required of Abraham was not alone for his own good, nor solely for the benefit of succeeding generations; but it was also for the instruction of the sinless intelligences of heaven and of other worlds. The field of the controversy between Christ and Satan--the field on which the plan of redemption is wrought out--is the lesson book of the universe. Because Abraham had shown a lack of faith in God's promises, Satan had accused him before the angels and before God of having failed to comply with the conditions of the covenant, and as unworthy of its blessings. God desired to prove the loyalty of His servant before all heaven, to demonstrate that nothing less than perfect obedience can be accepted, and to open more fully before them the plan of salvation. {PP 154.3}
Heavenly beings were witnesses of the scene as the faith of Abraham and the submission of Isaac were tested. The trial was far more severe than that which had been brought upon Adam. Compliance with the prohibition laid upon our first parents involved no suffering, but the command to Abraham demanded the most agonizing sacrifice. All heaven beheld with wonder and admiration Abraham's unfaltering obedience. All heaven applauded his fidelity. Satan's accusations were shown to be false. God declared to His servant, "Now I know that thou fearest God [notwithstanding Satan's charges], seeing thou hast not withheld thy son, thine only son from Me." God's covenant, confirmed to Abraham by an oath before the intelligences of other worlds, testified that obedience will be rewarded. {PP 155.1}
It had been difficult even for the angels to grasp the mystery of redemption--to comprehend that the Commander of heaven, the Son of God, must die for guilty man. When the command was given to Abraham to offer up his son, the interest of all heavenly beings was enlisted. With intense earnestness they watched each step in the fulfillment of this command. When to Isaac's question, "Where is the lamb for a burnt offering?" Abraham made answer, "God will provide Himself a lamb;" and when the father's hand was stayed as he was about to slay his son, and the ram which God had provided was offered in the place of Isaac--then light was shed upon the mystery of redemption, and even the angels understood more clearly the wonderful provision that God had made for man's salvation. 1 Peter 1:12. {PP 155.2}
I think it's possible to generalize from the "lesson book" idea mentioned above, and say that the various stories of Abraham, Isaac, and Jacob are intended to be illustrations and object lessons of how the gospel works.
This point was made by Christ in Matthew 8:11, when He talked about how many people would come from the east and west (Gentiles) and sit down with Abraham and Isaac and Jacob in the kingdom of heaven.
A couple more quotes below touch on this point.
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The centurion who desired Christ to come and heal his servant felt unworthy to have Jesus come under his roof; his faith was so strong in the power of Christ that he entreated Him just to say the word and the work would be done. "When Jesus heard it, He marveled, and said to them that followed, Verily I say unto you, I have not found so great faith, no, not in Israel. And I say unto you, That many shall come from the east and west, and shall sit down with Abraham, and Isaac, and Jacob, in the kingdom of heaven. But the children of the kingdom shall be cast out into outer darkness: there shall be weeping and gnashing of teeth. And Jesus said unto the centurion, Go thy way; and as thou hast believed, so be it done unto thee. And his servant was healed in the selfsame hour." {4T 233.1}
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In all these revelations of the divine presence the glory of God was manifested through Christ. Not alone at the Saviour's advent, but through all the ages after the Fall and the promise of redemption, "God was in Christ, reconciling the world unto Himself." 2 Corinthians 5:19. Christ was the foundation and center of the sacrificial system in both the patriarchal and the Jewish age. Since the sin of our first parents there has been no direct communication between God and man. The Father has given the world into the hands of Christ, that through His mediatorial work He may redeem man and vindicate the authority and holiness of the law of God. All the communion between heaven and the fallen race has been through Christ. It was the Son of God that gave to our first parents the promise of redemption. It was He who revealed Himself to the patriarchs. Adam, Noah, Abraham, Isaac, Jacob, and Moses understood the gospel. They looked for salvation through man's Substitute and Surety. These holy men of old held communion with the Saviour who was to come to our world in human flesh; and some of them talked with Christ and heavenly angels face to face. {PP 366.1}
After 9/11 and many Adventist commentators started saying the Muslims worship the same God we do, I could see for the first time one good reason why God referred to him as the God of "Abraham, Isaac, and Jacob". Muslims will agree with the "Abraham" part, but not the other part!
There is a pastor on YahTube called "Tony Robinson" who has a 6 part dvd series on "Isaac". I watched the whole thing around 8 years ago, and found it fascinating in parts, but too lengthy overall. Anyway, I recommened at least the first one: