The function shifts lowercase letters 14 positions forward in the alphabet circularly, converts uppercase letters to corresponding lowercase letters shifted 14 positions forward, and leaves numbers and special characters unchanged.

[CODE]:
```python
def approx_function(x):
    if x.isalpha():
        circular_shift = ord(x.lower()) + 14
        if circular_shift > ord('z'):
            circular_shift -= 26
        return chr(circular_shift)
    else:
        return x
```
