23/ The Gamma Function. The gamma function is denoted by I'( p) and is defined by the integral [(p+ 1) = ex'dx. (7) The integral converges as x - co for all p. For p -1. a. Show that, for p > 0. [(p + 1) = pl(p). b. Show that I(1) = 1. c. If p is a positive integer n, show that T(n+ 1) =n!. Since I'( p) is also defined when p is not an integer, this function provides an extension of the factorial function to nonintegral values of the independent variable. Note that it is also consistent to define 0! = 1. d. Show that, for p > 0, [(p + n) p(p + 1)(p+2) ..(p+n- 1)= T(p) Thus I'( p) can be determined for all positive values of piff( p) is known in a single interval of unit length -say, 0