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

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 $
$ \{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 $
$ J $
$ \text{Region} $

Calculation

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

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