Read the PHP manual about the 'pconnect' versions of database connections.
They do the connection pooling.
Note that using persistant connections will increase the average number of connections that are open at any given time when compared to
using normal connections. This will consume more resources for longer periods of time than using normal connections, and the only (only) benefit is that the database connections have to be opened fewer times because they are closed fewer times.
If you have the resources to keep lots of connections open, do it.
Otherwise, don't.