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Second partial derivative of $γ^r$ with respect to $τ$

Values for calculation

$n_i$
$π$
$I_i$
$J_i$
$τ$
$\text{Region}$

Calculation

Second partial derivative of $ γ^r $ with respect to $ τ $

$\text{if }\ \text{Region}= 2$
$$γ^r_{ττ}=\sum_{i=1}^{43}{n_i\cdot π^{I_i}\cdot J_i\cdot\left(J_i-1\right)\cdot\left(τ-0.5\right)^{J_i-2}}$$
$\text{else if }\ \text{Region}= 5$
$$γ^r_{ττ}=\sum_{i=1}^{6}{n_i\cdot π^{I_i}\cdot J_i\cdot\left(J_i-1\right)\cdot τ^{J_i-2}}$$
$\text{else}$
$$γ^r_{ττ}=0$$