Email notification

I'm sorry if I've asked a dumb question or one that has been asked before (I searched the archives, but. . . ).

My question is about email notification. I notice that my iPhone notifies me with a sound immediately when I receive a new Gmail email, but it doesn't notify me with a sound when I receive an email from Comcast (POP3). I have to go into the mail application and tap the tab for this email account to see whether I've received any mail. Is there a way to have the iPhone notify me of new emails for both types of accounts? I've tried the Ultimate Notifier app, but it doesn't work like that. Please advise.

Thanks in advance.