7-48. Given the gamma function (7.42), use integration by parts to demonstrate that:

(a) (α) = (α − 1)(α − 1)

(b) If α is a positive integer, (α) = (α − 1)(α − 2) . . . 2 · 1(1)

(c) (1) = 1

(d) (α) = (α − 1)!