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

Values for calculation

$ n $
$ \{δ\in\mathbb{R}\mid δ>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ δ $
$ I $
$ J $
$ \{τ\in\mathbb{R}\mid τ>0\} $
This set includes all real numbers that are greater than zero. Therefore, it contains only positive numbers. Zero and negative numbers are not included in this set.
$ 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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