Four hundred years after the Buddha passed away, in the southern country of Vidarbha, there lived a prosperous Brahmin who was childless. In a dream, gods foretold that if he invited one hundred Brahmins to a religious festival, a son would be born to him. He did as he was told, made prayers, and ten months later a son was born. When he showed the child's distinguishing marks to one who could discern omens, he was told that though the child had excellent marks, he would not live more than one week. [The father] then asked what could help his son. He was instructed that if he invited one hundred Brahmins to a religious festival, his son would live seven months, and if he invited one hundred monks to such an event, the child would live seven years, yet it was impossible for him to live longer than that.
The father did as he was told. When the seven-year period drew near, the parents, who couldn't bear the thought of seeing their son's dead body, sent him off to travel, accompanied by a servant. On his travels, the child saw the face of [Bodhisattva] Khasarpana and later arrived at the gates of glorious Nalanda Monastery. There, he recited aloud the poetry of the Vedas, which was heard by the resident Brahmin Saraha. Saraha brought him inside, where the boy related his circumstances. Master [Saraha] said, "If you are able take ordination as a monk, I have the means [to prolong your life]." Thus he took ordination. [Saraha] granted him empowerment within the sacred circle of Buddha of Infinite Life, Conqueror of the Lord of Death, and had him recite the mantra. In particular, the child recited the mantra during the evening and night of the final day of his seventh year and was freed from the Lord of Death. Then he was reunited with his parents, who were overjoyed.
Following that, he requested from Brahmin Saraha [empowerment and teaching in] texts along with the meditative instructions for such deities as Matrix of Mystery. He requested Rahulabhadra, the abbot of Nalanda, to be his preceptor and became fully ordained, known as the monk Shriman.
Serving as Advisor to Nalanda's spiritual community
While he served as an advisor to Nalanda's spiritual community, a great famine struck. Shriman obtained from Ling-bar [a place] an alchemical elixir that could produce gold, and having used it to make gold, he was able to acquire [enough food to provide for] the monastic community's midday meals: they were able to complete their monsoon-season retreat. The monks [leaving retreat] saw starving people and death and asked him, "How have you produced our midday meals during a famine?" When Shriman explained how he had done so, they replied, "Without asking the community, you had us [accept food gained from] wrong means of livelihood. We expel you and order you to construct ten million temples and stupas."
The Ornament of Awareness - 1,200,000 verses
Thereafter, he gained, through meditation practice, the attainment of both mundane and transcendent accomplishments. During this time, a monk named Shamkara composed a work entitled The Ornament of Awareness in 1,200,000 verses and disputed with everyone. To subdue [this challenge, Shriman] taught at Nalanda. Two boys listened to his teaching and left afterward, going underground. He asked who they were, and, when the boys told him, "We're nagas," he asked them to bring him clay from [the realm of] noxious spirits. They reported this to the naga king, who told them to invite the teacher. [Shriman] knew it would be beneficial [to accept] the invitation and went to the nagas' realm, where he taught the doctrine.
The Perfection of Sublime Insight
The nagas asked him to stay with them, but he replied, "I have come seeking clay with which to build ten million stupas and to take The Perfection of Sublime Insight in One Hundred Thousand Verses back [to the human realm]. I have no time to stay now, but it is possible that I will later return." He [departed,] taking with him a large amount of clay, as well as The Perfection of Sublime Insight in One Hundred Thousand Verses and The Perfection of Sublime Insight in a Few Words. It is said that the nagas did not give him a portion of the end part of The Perfection of Sublime Insight in One Hundred Thousand Verses. Thereafter, he used the clay to build the ten million stupas and other sacred supports and was assisted by most nagas, of whom some did not return to the naga realm and of whom he became their "mother." Thus, he became known by the name "Nagarjuna," Propitiator of Nagas.
Nagarjuna 'Propitiator of Nagas'
Thereafter, having used alchemy to produce gold in Pundravardhana, Nagarjuna distributed generous gifts. At that time, an old Brahmin couple, to whom he had given much gold, became faithful to Nagarjuna. The old man served as [Nagarjuna's] attendant and heard his teachings. After death, the man was reborn as the master Nagabodhi.
The Jewel Garland, written for a king
Nagarjuna then went to the eastern region of Patavesha, where he built many temples, and did likewise in the country of Radha. There was a particular rock that resembled a bell that he hoped to change to gold, but the gods prevented him from doing so. After that he went to the northern continent of Ominous Sound. On the way there, in the city of Salama, he met a young boy named Jitaka, and, from the lines on the boy's palm, [Nagarjuna] foretold that he would become a king. Having arrived at Ominous Sound, [Nagarjuna] hung his clothes on a tree and washed himself. While he did so, [the people of that continent] carried away his clothes. "Those are mine," he protested. They said, "He has an ‘I,' a self!" and stared at him. Then, after he had fulfilled his purposes there, he left. Meanwhile, the boy he had met had become a king and offered Nagarjuna many precious gems. In return, Nagarjuna gave him the precious teaching The Jewel Garland.
Letter to a Friend
This master served as teacher to the monastic community, built numerous stupas and monasteries, encircled Vajra Seat with a stone lattice fence, and constructed the setting of the glorious Dhanya-kataka Stupa. His treatises in the field of Buddhist inner knowledge include texts that emphasize the view, presenting the middle way beyond extremes from the perspective of the scriptures - A Collection of Praises, and those that present it from the perspective of reasoning - A Collection on Reasoning. Among his treatises that emphasize conduct, The Compendium of the Discourses presents it from the perspective of scripture; Training of the Mind in the Great Way, the perspective of reasoning; and Wish-Fulfilling Counsel on Dreams, which causes the awakening of affinity [with the conduct] of pious attendants. A Letter to a Friend emphasizes conduct for those whose support is [the vows of a] householder; The Awakened Assembly, the conduct of renunciations.
Among his treatises concerned with [secret] mantra, A Compendium of Tantras provides a brief exposition of [tantra's] view and conduct. Awakened Mind: A Commentary establishes the view. To present the phase of creation, he wrote Matrix of Mystery: Meditation Technique, a concise version of this, Matrix of Mystery: Blended with the Discourses, and Matrix of Mystery: Twenty-Part Sacred Circle Ritual. The Five Stages teaches the phase of completion.
His treatises on medicine include One Hundred Prescriptions. Among his works on secular customs, A Drop of Nourishment for Individuals contains advice for common people, One Hundred Verses on Knowledge contains advice for officials, and The Jewel Garland, written for a king, presents the integration of the great way's view and conduct. His many other original works include The Absolute Nature of the Science of Interdependent Arising, Aroma Prescriptions, and Transmutation into Gold. Those identified as his commentaries on others' texts include Matrix of Mystery Tantra: A Commentary and The Rice Province Discourse: A Commentary.
As for The Four Seals: A Presentation, Sheaves of Pith Instructions declares, "Nagarjuna did not write that text." Master Prajnakaramati states in Entering the Conduct of Bodhisattvas: A Major Commentary that Master Nagarjuna composed a text The Compendium of Training [as had Shantideva].
In these ways, Nagarjuna worked on behalf of the doctrine for six hundred years.
During that time, King Antivahana or Udayanabhadra had a son, Prince Shaktiman. When his mother gave him a fine seamless mantle, the boy said, "I will need this when I rule the kingdom." His mother replied, however, "You shall never rule the kingdom. Your father and Master Nagarjuna used longevity practice and extracting the essence of matter to gain accomplishment: [your father's] life shall be as long as the Master's." The prince then went to Master Nagarjuna's residence on Shriparvata Mountain. Raising his head, [Nagarjuna] ordered the prince to cut it off, but his sword could not sever his neck. The master said, "I have the ripened karma of having cut an insect with a blade of kusha grass and caused its death. Cut with kusha grass." [The prince] cut off [Nagarjuna's head]; this verse issued from the base of his neck:
I have gone to Blissful Realm,
But I will once again enter this body.
As the prince left carrying the head, a female noxious spirit snatched it from him and threw it one league away [from the body]. Neither the head nor the body decay, but with each passing year draw nearer to one another. It is said that when they eventually rejoin, Nagarjuna will work for the benefit of the doctrine and of beings.
[In the name] Nagarjuna, naga signifies birth from the basic space of phenomena, abiding in neither the extreme of eternalism or nihilism, mastery over the vault of precious scriptures, and being endowed with the view that burns and illuminates. Arjuna signifies one who has procured worldly power. Thus, he is named Arjuna because he governs the kingdom of the doctrine and subdues the hosts of faulty enemies. Taken together, these two parts form the name "Nagarjuna."
The Fundamental Verses on Sublime Insight - A Commentary: Clear Words states:
I bow to Nagarjuna,
He who has eliminated resting in either of the two extremes
And who gained birth in the ocean of the perfect Buddha's intellect;
Who compassionately teaches according to his realization
Of the treasury of the sacred doctrine's profundity as it is;
Whose view is a blazing mass of fire
That now consumes the firewood
Of opposing scriptural traditions,
And overcomes the world's mental darkness.
His quiver of arrows, non-dual wisdom speech,
Unleashed in this world of his disciples, including the gods,
Perfectly accomplishes his sovereignty in the three realms,
And triumphs over all legions of mundane enemies.
Composed by the Bodhisattva Nagarjuna who departed to the Realm of Bliss,
Having, out of compassion, severed his head and bestowed it to he who came seeking it.
Some contend that The Great Cloud Discourse states,
Four hundred years after I have passed away, this Licchavi [clan member] will become a monk called Naga. He will cause my doctrine to flourish and ultimately become Buddha Light of the Source of Wisdom in a world called Light of Purity.
The Great Cloud Discourse states:
In the southern region of Rishila, a king named Repairing Decline will appear. During his reign, when the king reaches eighty years of age, the sacred doctrine will be destroyed, leaving but a few remnants behind. At that time, on the northern shore of the mountain stream called Beautiful Wealth in the meritorious town known as Mahavaluka, in the vicinity of the land that belonged to the aristocrat Drago-chen, a young Licchavi [clan member] bearing my name, the sight of whom delights the entire world, will be born to spread the doctrine. In the presence of Transcendent Buddha Lamp of the Naga Family, this youth will vow to forsake his life on behalf of the doctrine and the Buddha's teachings. It is he who will propagate the doctrine.
So it reads. While it can be said that Nagarjuna is not explicitly mentioned, it must be examined based on some persons' belief that Nagarjuna's [formal Buddhist name] was Shakyamitra. It is also said that Nagarjuna's life is extensively foretold in The Great Drum Discourse, but this too must be researched.
Read more about Nagarjuna here.