(a) If f(t) = tm and g(t) = tn, where m and n are positive integers, show thatf g =

Chapter 6, Problem 12

(choose chapter or problem)

(a) If f(t) = tm and g(t) = tn, where m and n are positive integers, show thatf g = tm+n+1 10um(1 u)n du.(b) Use the convolution theorem to show that 10um(1 u)n du = m! n!(m + n + 1)!.(c) Extend the result of part (b) to the case where m and n are positive numbers but notnecessarily integers.

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