Persona 3 The Movie #1 Spring of Birth is the first of an upcoming animated movie series based on the game Shin Megami Tensei: Persona 3. There is currently no release date other than the ambiguous Fall 2013. Its official Twitter account currently updates every full moon with some information about the movie.
Persona 3: The Movie #1 Spring of Birth is going to come out. There is no release date, as it says above, but hopefully coming out in this fall.
Here is PV 1 of Persona 3: The Movie #1 Spring of Birth.