Rif Rosh HaShana 12b {Eruvin 40a continues; 40b}

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{Eruvin 40a continues}
it was a question to us: Should one mention {in prayers} Rosh Chodesh on Rosh haShana? Since they are distinct in their respective mussaf offerings {and we bring both}, we should say, or perhaps he can make a single remembrance and it will count for him both this way and that?
And we conclude: He says a single remembrance and it counts for him this way and that.

{Eruvin 40b}
And Rava said: When we were in the house of Rav Huna {=the academy at Sura}, it was a question to us: Should one say zeman {=Shehechiyanu} on Rosh HaShana and Yom Kippur? For since it comes from time to time, we should say it? Or perhaps since they {Rosh haShana and Yom Kippur} are not called regalim, we do not say?
He had no answer.
When he came to the house of Rav Yehuda {=the academy of Pumpedita; while Rav Huna at Sura was Rosh Yeshiva after Rav, Rav Yehuda founded Pumpedita after Nehardea, the academy of Shmuel, was destroyed. Thus, we are dealing with teachings from the two competing academies.} he said to him: {even} on a new gourd I also say Shehechiyanu.
He said to him: I am not asking if one is permitted {to say Shehechiyanu}. Is is an obligation?

And the conclusion is that the halacha is that one says Shehechiyanu on Rosh haShana and Yom Kippur.

END PEREK FOUR (yom tov)
END ROSH HASHANA