
The function seems to increment the second character of a given string by 2 if the character is an alphabetic letter in the English alphabet. For other characters such as digits and special characters, the function keeps them as they are. If the incremented character goes beyond 'z', the incrementation wraps around back to 'a'.

[CODE]: 
```python
def approximation_function(input_string):
    if len(input_string) < 2:
        return input_string

    second_character = input_string[1]
    
    if second_character.isalpha():
        new_char = chr(((ord(second_character) - ord('a') + 2) % 26) + ord('a'))
    else:
        new_char = second_character
    
    return input_string[0] + new_char + input_string[2:]
```
Please note that this is an approximation of the original function's behavior, and there might be variations depending on the inputs.