## Converting Mathematica Fourier series code to Python

Problem Description:

I have some simple Mathematica code that I’m struggling to convert to Python and could use some help:

```
a = ((-1)^(n))*4/(Pi*(2 n + 1));
f = a*Cos[(2 n + 1)*t];
sum = Sum[f, {n, 0, 10}];
Plot[sum, {t, -2 [Pi], 2 [Pi]}]
```

The plot looks like this:

For context, I have a function f(t):

I need to plot the sum of the first 10 terms. In Mathematica this was pretty straighforward, but for some reason I just can’t seem to figure out how to make it work in Python. I’ve tried defining a function a(n), but when I try to set f(t) equal to the sum using my list of odd numbers, it doesn’t work because t is not defined, but t is a variable. Any help would be much appreciated.

Below is a sample of one of the many different things I’ve tried. I know that it’s not quite right in terms of getting the parity of the terms to alternate, but more important I just want to figure out how to get ‘f’ to be the sum of the first 10 terms of the summation:

```
n = list(range(1,20,2))
def a(n):
return ((-1)**(n))*4/(np.pi*n)
f = 0
for i in n:
f += a(i)*np.cos(i*t)
```

## Solution – 1

modifying your code, look the part which are different, mostly the mistake was in the part which you are not calculating based on n 0-10 :

```
n = np.arange(0,10)
t = np.linspace(-2 * np.pi, 2 *np.pi, 10000)
def a(n):
return ((-1)**(n))*4/(np.pi*(2*n+1))
f = 0
for i in n:
f += a(i)*np.cos((2*i +1) * t)
```

however you could write you could in matrix form, and avoid looping, using the vector and broadcasting:

```
n = np.arange(10)[:,None]
t = np.linspace(-2 * np.pi, 2 *np.pi, 10000)[:,None]
a = ((-1) ** n) * 4 / (np.pi*(2*n + 1))
f = (a * np.cos((2 * n + 1) * t.T )).sum(axis=0)
```