Problem 4. Gamma function continued. (a) Let w2 = r. Show that [(a) =2 2-le-u' du and hence that To)(s) =43-le 2 20-le dudu. (b) Now let u = recs(0) and v =r sin(#). Show that pan+28-le-'cos30-1(0)sin28-1(0) drd9 (c) Now let r = cos-(0). Show that 2 cos 20-1(0)sin 23-1(0)de = / 20-1(1-2)-'dx. (d) Using the previous two parts show that 20-(1 -2)8-1dr = r(a)T (8) T(a + B) (e) Using the previous two parts show that I(]) = Va