The gamma function, which plays an important role in advanced applications, is defined
Chapter 7, Problem 101(choose chapter or problem)
The gamma function, which plays an important role in advanced applications, is defined for n 1 by (n) = 0 t n1et dt (a) Show that the integral defining (n) converges for n 1 (it actually converges for all n > 0). Hint: Show that tn1et < t2 for t sufficiently large. (b) Show that (n + 1) = n (n) using Integration by Parts. (c) Show that (n + 1) = n! if n 1 is an integer. Hint: Use (b) repeatedly. Thus, (n) provides a way of defining n-factorial when n is not an integer
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