The following is a recursive Python function:

The provided recursive function can be analyzed as follows:

- When `n` is 1, the function returns 3.
- For any other value of `n`, the function calls itself with `n - 1` and adds 3 to the result.

This means that the function calculates:

- For `n = 1`: `mystery(1) = 3`
- For `n = 2`: `mystery(2) = mystery(1) + 3 = 3 + 3 = 6`
- For `n = 3`: `mystery(3) = mystery(2) + 3 = 6 + 3 = 9`
- For `n = 4`: `mystery(4) = mystery(3) + 3 = 9 + 3 = 12`
- And so on...

We can see that for `n`, the function returns \(3 + 3(n - 1)\). This is because each reduction in `n` adds 3, effectively making it \(3 \times n\).

Thus, the mathematical function defined by this recursive function is:

**3 times n** (or mathematically represented as \(3n\)).