Nitzevet bat Adael[1][2] (Hebrew: נִצֶּבֶת בַּת עַדְאֵל Nīṣṣeḇeṯ baṯ ʿAḏʾēl) is, according to Hanan bar Rava, the mother of David with her husband Jesse and is the daughter of Adael, according to the Talmud.[3][unreliable source?] According to the Bible, Jesse had at least nine children: Eliab, Abinadab, Shimma, Nethaneel, Raddai, Ozem, David, Zeruiah, and Abigail.[4][5]
Zeruiah and Abigail are mentioned in the bible (2 Sam. 17:25), "Amasa was the son of a man named Jether, an Israelite who had maried Abigail, the daughter of Nahash and sister of Zeruiah the mother of Joab." However, since this text would indicate that the father of Abigail and Zeruiah is Nahash rather than Jesse, it would appear that their unnamed mother married Jesse after the death of Nahash (2 Sam. 10, 1 Sam. 11). Therefore, these women are not Jesse's daughters but half-sisters of David through Nahash's widow. It is not clear if this widow is the same Netzevet unless you conclude that she is indeed the mother of Zeruiah and Abigail as well.
Although David's mother is not named in the Bible, she is still mentioned there with her husband: when David was worried about the safety of his parents, he went to Mizpah in Moab to ask permission from the king to allow his father and mother to stay under the royal protection of the king:
And David went thence to Mizpeh of Moab; and he said unto the king of Moab: 'Let my father and my mother, I pray thee, come forth, and be with you, till I know what God will do for me.'
— 1 Samuel 22:3-4[6]
In a few Bible translations, Psalm 86:16 (attributed to David) mentions the writer's mother:
Show that you hear me and be kind to me.
I am your servant, so give me strength.
I am your slave, as my mother was, so save me! — Psalms 86:16[7]