 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-3/7e/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

z \to 0

Γ (1 + z) = z Γ (z)

and continuity at

1

give

Γ (z) \sim \frac{1}{z}, Γ (2 z) \sim \frac{1}{2 z} .

Using part (a),

B (z, z) = \frac{Γ ( z ) ^{2}}{Γ ( 2 z )} \sim \frac{z ^{- 2}}{( 2 z ) ^{- 1}} = \frac{2}{z} .

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