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Cross derivative of $γ^o$ with respect to $π$ and temperature $τ$

Values for calculation

$ \text{Region} $

Calculation

Cross derivative of $ γ^o $ with respect to $ π $ and temperature $ τ $

$\text{if }\ \text{Region}= 2$
$$γ^o_{πτ}=0$$
$\text{else if }\ \text{Region}= 5$
$$γ^o_{πτ}=0$$
$\text{else}$
$$γ^o_{πτ}=0$$