Question

Which of the following is true?

(a) Γ(n+1) = nΓ(n) for any real number

(b) Γ(n) = nΓ(n+1) for any real number

(c) Γ(n+1) = nΓ(n) for n>1

(d) Γ(n) = nΓ(n+1) for n>1

I have been asked this question in an interview for job.

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

Answer 1

The correct answer is (c) Γ(n+1) = nΓ(n) for n>1

To explain: Γ(n+1) = n! = n. (n-1)! = n.Γ(n). Hence Γ(n+1) = nΓ(n) for n>1.