MediumCalculusca-122

Digamma Approximation

Problem

For a positive integer n, the digamma function satisfies psi(n) = -gamma + H_{n-1}, where gamma = 0.5772156649015329 is the Euler-Mascheroni constant and H_{n-1} is the (n-1)-th harmonic number.

Given n >= 1, return psi(n) using this exact integer formula.

Hint

psi(1) = -gamma and psi(n+1) = psi(n) + 1/n.

Test cases

case 1

in: [1]

expected: -0.5772156649015329

case 2

in: [2]

expected: 0.42278433509846713

case 3

in: [5]

expected: 1.5061176684318005

case 4

in: [10]

expected: 2.2517525890667214

Starter codePython

def digamma_integer(n):
    # Your code here
    pass

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