Discussion
Consider the following statements about the gamma function. 1. It extends the factorial to non-integer arguments 2. \( \Gamma(1/2) = \sqrt{\pi} \) 3. It satisfies \( \Gamma(n) = n\,\Gamma(n+1) \)
Answer: C
The first two hold. The third has the recursion inverted: the correct relation is \( \Gamma(n+1) = n\,\Gamma(n) \), so the gamma of the *larger* argument carries the factor. Written the other way it would make the function decrease along the integers instead of growing like the factorials
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