Can every recursion be converted into iteration?

Question

A reddit thread brought up an apparently interesting question:

Tail recursive functions can trivially be converted into iterative functions. Other one

Answer 1

Have a look at the following entries on wikipedia, you can use them as a starting point to find a complete answer to your question.

• Recursion in computer science
• Recurrence relation

Follows a paragraph that may give you some hint on where to start:

Solving a recurrence relation means obtaining a closed-form solution: a non-recursive function of n.

Also have a look at the last paragraph of this entry.