The function shifts letters (both lowercase and uppercase) 4 positions forward in the alphabet, leaving numbers and special characters unchanged.

[CODE]:
```python
def approx_function(s):
    result = ""
    for c in s:
        if c.isalpha():
            shift = 4
            if c.islower():
                result += chr(((ord(c) - ord('a') + shift) % 26) + ord('a'))
            else:
                result += chr(((ord(c) - ord('A') + shift) % 26) + ord('A'))
        else:
            result += c
    return result
```

Keep in mind that this is an approximation of the original function and may have slight differences.