Apple doesn’t allow you to manage your purchases. Patently absurd really. When you’ve lost your iPhone apps as I have done on occasion here is how you can laboriously and tediously recover them.
Launch iTunes. Select Store > View my account
Provide the credentials for your Apple Account and then select Purchase History.
Now you can page through your iTunes purchases and laboriously search > install and then repeat every one of the previous steps. I am sure you will enjoy this superlative Apple user experience as much as I have.
Since I could not find this in my Google searches allow me to include the following SEO: install iPhone apps, reinstall iPhone apps, re-install iPhone apps, recover iPhone applications.
Thank you @gigowey for the timely assist.
You have to love Twitter.
Aaron Fulkerson 
Thanks for posting this. Come on Apple make this easier for us !!!!