MediumCalculusca-082

Beta Function Value

Problem

Evaluate the beta function B(a, b) = Gamma(a) * Gamma(b) / Gamma(a + b) using the gamma recursion for integer and half-integer arguments.

Define a local gamma helper with Gamma(1) = 1 and Gamma(0.5) = sqrt(pi), then combine the three values.

Hint

For integers, B(a, b) reduces to (a-1)! (b-1)! / (a+b-1)!.

case 1

in: [1,1]

expected: 1

case 2

in: [2,3]

expected: 0.08333333333333333

case 3

in: [0.5,0.5]

expected: 3.1415926535897927

case 4

in: [3,3]

expected: 0.03333333333333333

case 5

in: [1,5]

expected: 0.2

Starter codePython

def beta_value(a, b):
    # Your code here
    pass

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