Interpreting formulas with ΣΣ (two sigma) in Python

Question

Consider the function f(x,y) that equals two sigma (ΣΣ) where i ranges from 1 to 10 and (first sigma) and j ranges from 1 to 10 (second sigma) of the quantity {ix^2 + jy^3)

I believe the first sigma would be an inner loop and the second sigma an outer loop, but I am having trouble rewriting this into Python.

How can I convert this into Python?

Answer 1

I'm no mathematician, but as far as I could tell, that would translate to

def f(x, y):
    return sum(
        sum(
            i * x ** 2 + j * y ** 3
            for j in range(1, 11)
        )
        for i in range(1, 11)
    )

or written out as for loops,

def f(x, y):
    value = 0
    for i in range(1, 11):
        for j in range(1, 11):
            value += i * x ** 2 + j * y ** 3
    return value