10. a. If f(t) = t" and g(t) = t", where m and n are posit integers, show that L'₁ f* g = fm+n+1 u" (1-u)" du. b. Use the convolution theorem to show that m!n! S (m+n+1)! c. Extend the result of part b to the case where m and n um (1 - u)" du

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Chapter2: Second-order Linear Odes
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10. a. If f(t) = t" and g(t) = t", where m and n are positive
integers, show that
f* g = fm+n+1
L₁
S
b. Use the convolution theorem to show that
m!n!
(m+n+1)!
u" (1-u)" du.
um (1 - u)" du
c. Extend the result of part b to the case where m and n are
positive numbers but not necessarily integers.
Transcribed Image Text:10. a. If f(t) = t" and g(t) = t", where m and n are positive integers, show that f* g = fm+n+1 L₁ S b. Use the convolution theorem to show that m!n! (m+n+1)! u" (1-u)" du. um (1 - u)" du c. Extend the result of part b to the case where m and n are positive numbers but not necessarily integers.
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