Question

β(m, n) = β(n, m). Is the statement true?

(a) True

(b) False

This question was posed to me during an internship interview.

The question is from Special Functions topic in section Special Functions – Gamma, Beta, Bessel and Legendre of Engineering Mathematics

Answer 1

Right choice is (a) True

For explanation: L.H.S. = \(\beta(m, n) = \frac{\Gamma(m).\Gamma(n)}{\Gamma(m+n)}. \)

R.H.S. \( = \beta(n, m) = \frac{\Gamma(n).\Gamma(m)}{\Gamma(n+m)} = \frac{\Gamma(m).\Gamma(n)}{\Gamma(m+n)} = \) L.H.S.

Therefore, \(\beta(m, n) = \beta(n, m).\)