The function appears to shift the alphabetical characters in the input string one position forward in the alphabet, while keeping numerical and special characters unchanged.

[CODE]: 
```python
def approx_function(input_str):
    result = ""
    for char in input_str:
        if char.isalpha():
            if char == 'z':
                result += 'a'
            elif char == 'Z':
                result += 'A'
            else:
                result += chr(ord(char) + 1)
        else:
            result += char
    return result
```
Please, let me know if you'd like me to test the function further or make any adjustments to the description and code provided.