 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2006/iii/paper-67/2/a/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

t_{n}

of degree at most

n

[- n, n]

s_{j} (t_{n})

therefore equals

t_{n}

for every

j \geq n

. Averaging the sums with

j = n, \dots, n + m - 1

gives

v_{n, m} (t_{n}) = \frac{1}{m} j = n \sum n + m - 1 t_{n} = t_{n} .

Thus the de la Vallée Poussin sum reproduces the entire degree-at-most-

n

approximation space, including when the actual degree is smaller.

 New to topics? Read the docs here!