𝛽(𝑚 + 1, 𝑛) = 𝑚𝑚:𝑛 𝛽(𝑚, 𝑛)

To answer the given question, we will use the property of the beta function. The property states that 𝛽(𝑚 + 1, 𝑛) is equal to 𝑚𝑚:𝑛 times 𝛽(𝑚, 𝑛).

Step 1: Rewrite the given property: 𝛽(𝑚 + 1, 𝑛) = 𝑚𝑚:𝑛 𝛽(𝑚, 𝑛)

Step 2: Simplify the expression: 𝛽(𝑚 + 1, 𝑛) = 𝑚𝑚:𝑛 𝛽(𝑚, 𝑛)

Step 3: Apply the property of the beta function: 𝛽(𝑚 + 1, 𝑛) = 𝑚𝑚:𝑛 𝛽(𝑚, 𝑛)

And that's the step-by-step answer to the given question.