Creating a new function as return in python function?

While I cannot give you an answer specific to what you plan to do. (Looks like math out of my league.)

I can tell you that Python does support first-class functions.

Python may return functions from functions, store functions in collections such as lists and generally treat them as you would any variable.

Cool things such as defining functions in other functions and returning functions are all possible.

>>> def func():
...     def func2(x,y):
...         return x*y
...     return func2
>>> x = func()
>>> x(1,2)
2

Functions can be assigned to variables and stored in lists, they can be used as arguments for other functions and are as flexible as any other object.

You should be able to do this by defining a new function inline:

def fourier_series(f, N):
    def F(x):
        ...
    return F

You are not limited to the arguments you pass in to fourier_series:

def f(a):
    def F(b):
        return b + 5
    return F

>>> fun = f(10)
>>> fun(3)
8