Question

What is the value of \(\beta(\frac{1}{4},\frac{3}{4})\)?

(a) \(\pi \)

(b) \(\sqrt{2}\pi \)

(c) \(\sqrt{2\pi} \)

(d) \({2}\pi \)

I have been asked this question at a job interview.

I need to ask this question from Special Functions in chapter Special Functions – Gamma, Beta, Bessel and Legendre of Engineering Mathematics

Answer 1

The correct choice is (b) \(\sqrt{2}\pi \)

The best I can explain: \(\beta(\frac{1}{4}, \frac{3}{4}) = \frac{\Gamma(\frac{1}{4}).\Gamma(\frac{3}{4})}{\Gamma(\frac{1}{4}+\frac{3}{4})} \)

\( = \frac{\pi}{sin⁡ \frac{π}{4}}  = \sqrt{2}\pi. \)