MediumCalculusca-081

Gamma Function Values

Problem

Evaluate the gamma function at positive integers and half-integers using the recursion Gamma(x + 1) = x * Gamma(x) with base values Gamma(1) = 1 and Gamma(0.5) = sqrt(pi).

Reduce x by whole steps until x is 1 or 0.5, then return the accumulated product.

Hint

Gamma(n) = (n-1)! for integers, and each half-step multiplies by the preceding half-integer.

Test cases

case 1

in: [0.5]

expected: 1.7724538509055159

case 2

in: [5]

expected: 24

case 3

in: [2.5]

expected: 1.329340388179137

case 4

in: [1]

expected: 1

case 5

in: [3.5]

expected: 3.323350970447842

Starter codePython

def gamma_value(x):
    # Only integer and half-integer inputs are supported
    # Your code here
    pass

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