Euler’s integral definition of the gamma function* is
Convergence of the integral requires that x – 1 > –1, or x > 0. The recurrence relation
that we saw in Section 5.3 can be obtained from (1) by employing integration by parts. Now when x = 1,
and thus (2) gives
and so on. In this manner it is seen that when n is a positive integer,
For this reason the gamma function is often called ...
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