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Cross derivative of $φ$ with respect to $δ$ and temperature $τ$

Values for calculation

$n$
$I$
$δ$
$J$
$τ$
$\text{Region}$

Calculation

Cross derivative of $ φ $ with respect to $ δ $ and temperature $ τ $

$\text{if }\ \text{Region}= 3$
$\text{if }\ \text{Region}= 3$
Equations in LaTeX code
\text{if }\ \text{Region}= 3
$$φ_{δτ}=\sum_{i=2}^{40}{n[i]\cdot I[i]\cdot δ^{I[i]-1}\cdot J[i]\cdot τ^{J[i]-1}}$$
$φ_{δτ}=\sum_{i=2}^{40}{n[i]\cdot I[i]\cdot δ^{I[i]-1}\cdot J[i]\cdot τ^{J[i]-1}}$
Equations in LaTeX code
φ_{δτ}=\sum_{i=2}^{40}{n[i]\cdot I[i]\cdot δ^{I[i]-1}\cdot J[i]\cdot τ^{J[i]-1}}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$φ_{δτ}=0$$
$φ_{δτ}=0$
Equations in LaTeX code
φ_{δτ}=0
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