Q: I have downloaded TV series in Itunes, but they are not showing up

Hello there, simonlevett.

You may need to delete and redownload your purchased content if it's not playing in iTunes. The following Knowledge Base article shows how to delete your content:

How to delete content you've downloaded from the iTunes Store, App Store, iBooks Store, or Mac App Store

http://support.apple.com/kb/HT5772

Remember the following:

Before you delete an item, make sure you can download it again. If you can't or need to pay to download it again, back up the item before you delete it.

After you delete an item, it might still be visible if you can download it again from iTunes in the Cloud. The Download icon will appear next to these items. You can hide items available in iCloud and purchases from the Mac App Store.

Once you've followed those steps for your TV Show, then this article provides how to download the episodes you need again:

Download past purchases

http://support.apple.com/kb/ht2519

iTunes Store

1. Open iTunes and go to the iTunes Store.
2. Click Purchased in the Quick Links section.
   
3. Select the content type that you want to download (Music, Movies, TV Shows, Apps, or Books).
4. Select Not in My Library to view purchased content that isn't on your computer.
   
5. Find the item that you want to download. You can browse using the menu to the left. If you have more than 2,000 songs, you will see Recent Purchases instead of All Songs or Albums.
   
6. Click the Download icon next to the item you want to download.
   If an item is already in your library, the Download icon won't appear.

Thanks for reaching out to Apple Support Communities.

Cheers,

Pedro.