Supplication at the time of slaughter

It is narrated from Sayyiduna Jabir bin Abdullah (may Allah be pleased with them both) that the Messenger of Allah (peace and blessings be upon him) led the people in prayer on the Day of Sacrifice. When he had finished the sermon and the prayer, he called for a ram and slaughtered it with his own blessed hand, and said: 'Bismillahi wallahu akbar, Allahumma hadha 'anni wa 'an man lam yudahhi min ummati' "In the name of Allah, and Allah is the Greatest. O Allah, this is on my behalf and on behalf of whoever of my Ummah has not offered a sacrifice."

Ibn Abi Rafi' narrates from his father, and he from his grandfather, that the Messenger of Allah (peace and blessings be upon him) slaughtered his sacrificial animal and then said: "O Allah, this is on my behalf and on behalf of my Ummah."

It is narrated from Sayyiduna Abdullah bin Hisham (may Allah be pleased with him) that his mother, Zaynab bint Humayd, took him to the Messenger of Allah (peace and blessings be upon him) when he was small, and he (peace and blessings be upon him) passed his hand over his head and supplicated for him. He said: The Messenger of Allah (peace and blessings be upon him) used to sacrifice just one goat on behalf of all his family members. All these hadiths have authentic chains regarding the concession that one goat suffices on behalf of all the people whose number is not fixed, contrary to the assumption of those who think that it suffices on behalf of only one person.

It is narrated from Sayyiduna Ali (may Allah be pleased with him) that he sacrificed two rams, one ram on behalf of the Prophet (peace and blessings be upon him) and one on his own behalf, and said: The Messenger of Allah (peace and blessings be upon him) commanded me to sacrifice on his behalf, so I will always keep sacrificing on his behalf.
This hadith has an authentic chain (sahih al-isnad), but the two Shaykhs (Bukhari and Muslim) did not record it, and Abu al-Hasna' who appears in its chain is in fact al-Hasan bin al-Hakam al-Nakha'i.

It is narrated from Sayyiduna Thawban (may Allah be pleased with him) (the freed slave of the Messenger of Allah (peace and blessings be upon him)); he said: The Messenger of Allah (peace and blessings be upon him) slaughtered his sacrificial animal during a journey, then said: "O Thawban, prepare (preserve) its meat properly." So I kept feeding him from it until we reached Madinah.
This hadith has an authentic chain (sahih al-isnad), but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Jabir (may Allah be pleased with him); he said: On the day of Hudaybiyah we slaughtered seventy camels, one camel on behalf of ten people, and the Messenger of Allah (peace and blessings be upon him) said: "A group of people may share in a sacrificial animal."
This hadith is sahih (authentic) on the condition of Imam Muslim, but the two Shaykhs (Bukhari and Muslim) did not record it.