Rosh Hashanah 4b:13ראש השנה ד׳ ב:י״ג
The Gemara raises a question: But can’t you say that we say that the Eighth Day of Assembly is a Festival in and of itself only with regard to peh, zayin, reish, kuf, shin, beit, an acronym that stands for six unique aspects to the Eighth Day of Assembly. But with regard to the matter of redress for failing to bring a Festival peace-offering, everyone agrees that the Eighth Day of Assembly is still a day of redress for the first day of the festival of Sukkot.
Tosafot on Rosh Hashanah 4b:13:1תוספות על ראש השנה ד׳ ב:י״ג:א׳
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Chagigah 17a:7חגיגה י״ז א:ז׳
The Gemara continues to ask: You can say that when they said that The Eighth Day of Assembly is an independent pilgrimage Festival, this applies only to the issue of peh, zayin, reish, kuf, shin, beit, an acronym for the six halakhot that differentiate The Eighth Day of Assembly from the festival of Sukkot. But with regard to the redress of the Festival offerings, it is considered a day of redress for the first Festival day, as we learned in a mishna (9a): One who did not celebrate by sacrificing the Festival offerings on the first day of the Sukkot Festival can celebrate by sacrificing them throughout the pilgrimage Festival of Sukkot and on the last day of that Festival. If so, the question remains: Why do we not compare Shavuot to Sukkot and allow its offerings to be completed on all eight days?
Yoma 3a:1יומא ג׳ א:א׳
Peh, zayin, reish, kuf, shin, beit, an acronym for: Lottery [payis], as a new lottery is performed on that day to determine which priests will sacrifice the offerings that day, and the order established on Sukkot does not continue; the blessing of time [zeman]: Who has given us life, sustained us, and brought us to this time, is recited just as it is recited at the start of each Festival; Festival [regel], as it is considered a Festival in and of itself and there is no mitzva to reside in the sukka (see Tosafot); offering [korban], as the number of offerings sacrificed on the Eighth Day is not a continuation of the number offered on Sukkot but is part of a new calculation; song [shira], as the Psalms recited by the Levites as the offerings were sacrificed on the Eighth Day are not a continuation of those recited on Sukkot; blessing [berakha], as the addition to the third blessing of Grace after Meals and in the Amida prayer (see Tosafot) is phrased differently than the addition recited on Sukkot.