Consider the advancement operator equation below = a g(n)b h(n) q(A) fn where q(A) is a...

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Consider the advancement operator equation below = a g(n)b h(n) q(A) fn where q(A) is a polynomial in A (the advancement operator) and g, h are functions of n. Suppose that p' is a particular solution of q(A) fn g(n) and suppose that p" is a particular solution of q(A)fn h(n) Show that p ap bp" is a particular solution of the original advance- ment operator equation (Hint: The remark after Theorem 9.18 in Section 9.5 in the textbook might be useful) Consider the advancement operator equation below = a g(n)b h(n) q(A) fn where q(A) is a polynomial in A (the advancement operator) and g, h are functions of n. Suppose that p' is a particular solution of q(A) fn g(n) and suppose that p" is a particular solution of q(A)fn h(n) Show that p ap bp" is a particular solution of the original advance- ment operator equation (Hint: The remark after Theorem 9.18 in Section 9.5 in the textbook might be useful)