The Gamma Function. The gamma function is denoted by Γ(p) and is defined by the integral Γ(p 1)=∫0^∞ e^-x x^p d xThe integral converges as x →∞ for all p . For p-1 .(a) Show that for p>0 Γ(p 1)=p Γ(p)(b) Show that Γ(1)=1.(c) If p is a positive integer n, show that Γ(n 1)=n !since Γ(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