Negative factorial?

Algebra Level 2

Calculate ( − 1 2 ) ! \large \left(- \frac 12 \right)!


The answer is 1.772453850905516027298167.

James Watson by James Watson , 16, United Kingdom

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1 solution

Chew-Seong Cheong
Jul 18, 2020

Since gamma function Γ ( n + 1 ) = n ! \Gamma (n+1) = n! , ( − 1 2 ) ! = Γ ( − 1 2 + 1 ) = Γ ( 1 2 ) = π ≈ 1.77 \left(- \dfrac 12 \right)! = \Gamma \left(- \dfrac 12 + 1 \right) = \Gamma \left(\dfrac 12 \right) = \sqrt \pi \approx \boxed{1.77} .

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