ScalingStacks

Proof. [02XE]

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Proof.

This follows from formulae (7.4) and (7.11) with the function f(n)​(z)=(z−λ)​log⁡(z−λ)f^{(n)}(z)=(z-\lambda)\log(z-\lambda), a (n−k)(n-k)-th primitive of which is

f(k)​(z)=(z−λ)n−k+1(n−k+1)!​(log⁡(z−λ)−∑j=2n−k+11j).f^{(k)}(z)=\frac{(z-\lambda)^{n-k+1}}{(n-k+1)!}\left(\log(z-\lambda)-\sum_{j=2}^{n-k+1}\frac{1}{j}\right).

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