ScalingStacks

Lemma 4.20 . [045R]

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Lemma 4.20.

(Differential identities)

∂γp​3∂μ=−∂γp​4∂μ=2∂γ∂ηp,p=1,2,\frac{\partial\gamma_{p3}}{\partial\mu}=-\frac{\partial\gamma_{p4}}{\partial\mu}=2\frac{\partial\gamma}{\partial\eta_{p}},\quad p=1,2,

and morever

∂γp​3∂ηq=∂γq​3∂ηp,∂γp​4∂ηq=∂γq​4∂ηp,p,q=1,2.\frac{\partial\gamma_{p3}}{\partial\eta_{q}}=\frac{\partial\gamma_{q3}}{\partial\eta_{p}},\quad\frac{\partial\gamma_{p4}}{\partial\eta_{q}}=\frac{\partial\gamma_{q4}}{\partial\eta_{p}},\quad p,q=1,2.

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