For v > -1, let 0,2) = 0F1 (v+1;-) (ER). (a) Prove that if v > -1/2, then (2) = Blv +1/2,1/2), (1 23-1/3 cos () dt. (b) Prove that if a > 0,8 > 0, then where B v +1, a +8 (1 t)o-1428-1 Bla,B) 2 f(t) = (C) Prove that if a > 0, 3 > 0, then p(t) (xt) dt where B, B+1/2 2F3 v+1, a +B, a +8+1/2 (1 t)20-1428-1 B(2a, 28) p(t) = (Hint: In simplifying constants, use Legendre's duplication formula T(22) = 222-1 T(z)T(z +1/2).) V For v > -1, let 0,2) = 0F1 (v+1;-) (ER). (a) Prove that if v > -1/2, then (2) = Blv +1/2,1/2), (1 23-1/3 cos () dt. (b) Prove that if a > 0,8 > 0, then where B v +1, a +8 (1 t)o-1428-1 Bla,B) 2 f(t) = (C) Prove that if a > 0, 3 > 0, then p(t) (xt) dt where B, B+1/2 2F3 v+1, a +B, a +8+1/2 (1 t)20-1428-1 B(2a, 28) p(t) = (Hint: In simplifying constants, use Legendre's duplication formula T(22) = 222-1 T(z)T(z +1/2).) V