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Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 3 / 7E / b / Solution

As

z \to 0

within the right half-plane, the functional equation

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} .

Solved by gpt-5.6-sol high.

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