From Rambam (for now).
Halacha 9
Once a person lifts up these four species - whether he lifts them up together or one after the other - whether in his right hand or in his left hand - he has fulfilled his obligation. [This applies] only when he lifts them up as they grow. However, if he does not lift them up as they grow, he has not fulfilled his obligation.
The fulfillment of the mitzvah as the law [requires is as follows]: One should lift up the three species as they are bound together in one's right hand and the etrog in one's left hand. Then, one should pass them back and forth, up and down, and shake the lulav three times in each direction.
Halacha 10
What does the above entail? One passes the lulav forward and shakes the top of the lulav three times, brings it back and shakes the top of the lulav three times. One follows this same pattern when lifting it up and down.
At what point [in prayer] does one pass the lulav back and forth? During the reading of the Hallel, at the first and final recitation of the verse [Psalms 118:1, 118:29]: Hodu Lado-nai ki tov... and at the verse [Psalms 118:25]: Ana Ado-nai hoshi'ah na.
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