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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 $

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