Question

What is the value of \( \Gamma(\frac{9}{4})\)?

(a) \(\frac{5}{4} * \frac{1}{4} * \Gamma(\frac{1}{4}) \)

(b) \(\frac{9}{4} * \frac{5}{4} * \frac{1}{4} * \Gamma(\frac{1}{4}) \)

(c) \(\frac{5}{4} * \frac{1}{4} * \Gamma(\frac{5}{4}) \)

(d) \(\frac{1}{4} * \Gamma(\frac{1}{4}) \)

This question was posed to me in an interview for internship.

The origin of the question is Special Functions in chapter Special Functions – Gamma, Beta, Bessel and Legendre of Engineering Mathematics

Answer 1

Right answer is (a) \(\frac{5}{4} * \frac{1}{4} * \Gamma(\frac{1}{4}) \)

The best explanation: \(\Gamma(\frac{9}{4}) = \Gamma(1+\frac{5}{4}) = \frac{5}{4} * \Gamma(\frac{5}{4}) = \frac{5}{4} * \Gamma(1+ \frac{1}{4}) = \frac{5}{4} * \frac{1}{4} * \Gamma(\frac{1}{4}). \)