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Second partial derivative of $φ$ with respect to $τ$

Values for calculation

$n$
$δ$
$I$
$J$
$τ$
$\text{Region}$

Calculation

Second partial derivative of $ φ $ with respect to $ τ $

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