Question

Which of the following is not a definition of Gamma function?

(a) \(\Gamma(n) = n!\)

(b) \(\Gamma(n) = \int_{0}^{\infty} x^{n-1} e^{-x}dx\)

(c) \(\Gamma(n+1) = n\Gamma(n)\)

(d) \(\Gamma(n) = \int_{0}^{1} log \left({1 \atop y}\right)^{n-1}\)

The question was asked in unit test.

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

Answer 1

Correct answer is (a) \(\Gamma(n) = n!\)

To explain: Each and every option represents the definition of Gamma function except Γ(n) = n! as Γ(n+1) = n! if n is a positive number.