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The beta and gamma functions are related by \( B(m,n) = \)

  • A.\( \dfrac{\Gamma(m)}{\Gamma(n)} \)
  • B.\( \dfrac{\Gamma(m)\Gamma(n)}{\Gamma(m+n)} \)
  • C.\( \Gamma(m)\Gamma(n)\Gamma(m+n) \)
  • D.\( \dfrac{\Gamma(m+n)}{\Gamma(m)\Gamma(n)} \)

Answer: B

The relation is

\[ B(m,n) \;=\; \int_{0}^{1} x^{m-1}(1-x)^{n-1}dx \;=\; \frac{\Gamma(m)\Gamma(n)}{\Gamma(m+n)}, \]

which is what makes the beta integral computable in closed form. The reciprocal arrangement is the binomial coefficient's shape, not the beta function's

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