How can I find out what software I've bought in the App Store?
On iPhone


Open the App Store on your device.
Make sure you are signed in  the same Apple ID used for the original purchase.  
Tap Updates from the bottom navigation bar.  





Tap on Purchased on navigation bar





Tap Purchased on the resulting screen.
Locate the app in your Purchased tab. Tap the download button.




On iTunes 11


Open iTunes on your computer. 
Make sure that you have Show iTunes in the Cloud
Purchases enabled in your iTunes preferences by going to iTunes >
Preferences under the Store tab. Then, click OK. 
If you're already signed in, choose Store > Sign In, and enter your Apple ID
and password. 
After you've signed in, click the Library located in the upper-right of the iTunes Store. Navigate to your iTunes library for the respective content type you wish to using the content selector in the upper-left. Choose Apps to download apps. Locate the item or title you wish to download. Click the download icon to download that item. For instance, you will want yours to say Apps.




Note: The download icon for previously purchased movies is located to the right of the movie title. To download previously purchased apps and books, you'll need to navigate to the Purchased page under the Quick Links section in the iTunes Store.