Creating a new function as return in python function?

Question

I was wondering if it is possible in python to do the following:

def func1(a,b):
   return func2(c,d)

What I mean is that suppose I do something with a,b which leads to some coefficients that can define a new function, I want to create this function if the operations with a,b is indeed possible and be able to access this outside of func1.

An example would be a simple fourier series, F(x), of a given function f:

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

What I mean by this is I want to creat and store this new function for later use, maybe I want to derivate it, or integrate or plot or whatever I want to do, I do not want to send the point(s) x for evaluation in fourier_series (or func1(..)), I simply say that fourier_series creates a new function that takes a variable x, this function can be called later outside like y = F(3)... if I made myself clear enough?

Answer 1

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