Here is an outline of a proof. The full argument is quite long.

Step 1.If then

Reason: Let . Using the relations and , you can check that This is equal to because

Step 2.If m, n are positive integers then

Reason: In Step 1, let . Then .

Step 3.For and , Also,

Reason: Follows immediately from Step 2 because .

Step 4. .

Reason: Just add up all the relations in Step 3.

Finally, divide by to get the result.