How to document small changes to complex API functions?

You could automate the "specialization" of the original docstring with an addendum. For instance, pydoc is using the special attribute __doc__. You could write a decorator which automatically overrides the original function __doc__ with your addendum.

For instance:

def extend_docstring(original, addendum):
    def callable(func):
        func.__doc__ = original + addendum
        return func

    return callable


def complex_api_function(a, b, c):
    '''
    This is a very complex function.

    Parameters
    ----------
    a: int or float
        This is the argument A.
    b: ....
    '''
    print('do something')

@extend_docstring(
    complex_api_function.__doc__,
    '''
    Addendum
    --------
    Parameter a can also be a string
    '''
)
def my_complex_api_function(a, b, c):
    return complex_api_function(float(a), b, c)

or...

def extend_docstring(original):
    def callable(func):
        func.__doc__ = original + func.__doc__
        return func

    return callable


def complex_api_function(a, b, c):
    '''
    This is a very complex function.

    Parameters
    ----------
    a: int or float
        This is the argument A.
    b: ....
    '''
    print('do something')

@extend_docstring(complex_api_function.__doc__)
def my_complex_api_function(a, b, c):
    '''
    Addendum
    --------
    Parameter a can also be a string
    '''
    return complex_api_function(float(a), b, c)

If you run pydoc (pydoc3 -w my_module.py) it produces: preview of html generated by pydoc

Additional note: If you are using Python 3 you could use annotations to document the type(s) of your function parameters. It offers a lot of benefits, not only documentation. For instance:

from typing import Union

def my_complex_api_function(number_or_str: Union[int, float, str], *args, **kwargs):

I'd recommend something like the following:

def my_complex_api_function(number_or_str, *args, **kwargs):
    """This function is a light wrapper to `complex_api_function`.
    It allows you to pass a string or a number, whereas `complex_api_function` requires a 
    number. See :ref:`complex_api_function` for more details.

    :param number_or_str: number or str to convert to a number and pass to `complex_api_function`.
    :param args: Arguments to pass to `complex_api_function`
    :param kwargs: Keyword arguments to pass to `complex_api_function`
    :return: Output of `complex_api_function`, called with passed parameters
    """

This is clear and concise. But please also remember that, if using a documentation system like sphinx, to link the functions with :ref:`bob` or similar.