Question

What is the value of \(\beta(\frac{9}{2},3) \)?

(a) \(\frac{16}{1287} \)

(b) \(\frac{16}{1278} \)

(c) \(\frac{14}{1287} \)

(d) \(\frac{16}{127} \)

I have been asked this question in an online interview.

My query is from Special Functions topic in chapter Special Functions – Gamma, Beta, Bessel and Legendre of Engineering Mathematics

Answer 1

Right choice is (a) \(\frac{16}{1287} \)

The explanation is: \(\beta(\frac{9}{2},3) = \frac{\Gamma(\frac{9}{2})\Gamma(3)}{\Gamma(\frac{9}{2}+3)} \)

\( =  \frac{\Gamma(\frac{9}{2})2}{\frac{13}{2}*\frac{11}{2}*\frac{9}{2}*\Gamma(\frac{9}{2})}  = \frac{16}{1287}.\)