The gamma function is defined for all x > 0 by the rule (x) = , 0 t x1 et dt. (a) Find

Chapter 7, Problem 48

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The gamma function is defined for all x > 0 by the rule (x) = , 0 t x1 et dt. (a) Find (1) and (2). (b) Integrate by parts with respect to t to show that, for positive n, (n + 1) = n(n). (c) Find a simple expression for (n) for positive integers n.

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