 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-1/8/c/solution

Because

a_{0} \neq = 0

, the lowest-power equation from part (b) requires the indicial equation

4 σ^{2} - 8 σ + 3 = (2 σ - 1) (2 σ - 3) = 0.

The two candidate indicial roots are therefore

σ = \frac{1}{2} and σ = \frac{3}{2} .

Their difference is the integer one, so the smaller-root coefficient equation at

k = 1

needs examination rather than automatic division.

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