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

Values for calculation

$n$
$I$
$π$
$J$
$τ$
$\text{Region}$

Calculation

Cross derivative of $ γ^r $ 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
$$γ^r_{πτ}=\sum_{i=1}^{43}{n[i]\cdot I[i]\cdot π^{I[i]-1}\cdot J[i]\cdot\left(τ-0.5\right)^{J[i]-1}}$$
$γ^r_{πτ}=\sum_{i=1}^{43}{n[i]\cdot I[i]\cdot π^{I[i]-1}\cdot J[i]\cdot\left(τ-0.5\right)^{J[i]-1}}$
Equations in LaTeX code
γ^r_{πτ}=\sum_{i=1}^{43}{n[i]\cdot I[i]\cdot π^{I[i]-1}\cdot J[i]\cdot\left(τ-0.5\right)^{J[i]-1}}
$\text{else if }\ \text{Region}= 5$
$\text{else if }\ \text{Region}= 5$
Equations in LaTeX code
\text{else if }\ \text{Region}= 5
$$γ^r_{πτ}=\sum_{i=1}^{6}{n[i]\cdot I[i]\cdot π^{I[i]-1}\cdot J[i]\cdot τ^{J[i]-1}}$$
$γ^r_{πτ}=\sum_{i=1}^{6}{n[i]\cdot I[i]\cdot π^{I[i]-1}\cdot J[i]\cdot τ^{J[i]-1}}$
Equations in LaTeX code
γ^r_{πτ}=\sum_{i=1}^{6}{n[i]\cdot I[i]\cdot π^{I[i]-1}\cdot J[i]\cdot τ^{J[i]-1}}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$γ^r_{πτ}=0$$
$γ^r_{πτ}=0$
Equations in LaTeX code
γ^r_{πτ}=0
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