Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 3 / 17B / c

Table of contents
- Solution c

Solution

The three-term recurrence theorem with the displayed coefficients identifies

P_{n}

with the monic orthogonal polynomial

p_{n}

. Part (b) says its zeros are precisely the eigenvalues of the real symmetric Jacobi matrix

A_{n}

, and part (a) says those zeros are distinct and all belong to

(- 1, 1)

.

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