MediumCalculusca-083

Error Function Series

Problem

Evaluate the error function with its Maclaurin series to n terms:

erf(x) ≈ (2 / sqrt(pi)) * sum from k = 0 to n-1 of (-1)^k * x^(2k+1) / (k! * (2k+1))

Accumulate the terms iteratively. Large x or small n will be inaccurate because the series converges slowly.

Hint

Each term changes by a factor of -x^2 / (k+1); divide by 2k+1 before adding.

case 1

in: [0,5]

expected: 0

case 2

in: [1,20]

expected: 0.8427007929497149

case 3

in: [-1,20]

expected: -0.8427007929497149

case 4

in: [0.5,15]

expected: 0.5204998778130466

Starter codePython

def erf_series(x, n):
    # Your code here
    pass

4 test cases · run your code against them in the editor