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Cross derivative of γ^r with respect to π and temperature τ

Values for calculation

n
I
\{π\in\mathbb{R}\mid π>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.
π
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

Cross derivative of γ^r with respect to π and temperature τ

\text{if }\ \text{Region}= 2
\text{if }\ \text{Region}= 2
Equations in LaTeX code
\text{if }\ \text{Region}= 2
γ^r_{πτ}=\sum_{i=1}^{43}{n[i]\cdot I[i]\cdot π^{I[i]-1}\cdot J[i]\cdot\left(τ-0.5\right)^{J[i]-1}}
γ^r_{πτ}=\sum_{i=1}^{43}{n[i]\cdot I[i]\cdot π^{I[i]-1}\cdot J[i]\cdot\left(τ-0.5\right)^{J[i]-1}}
Equations in LaTeX code
γ^r_{πτ}=\sum_{i=1}^{43}{n[i]\cdot I[i]\cdot π^{I[i]-1}\cdot J[i]\cdot\left(τ-0.5\right)^{J[i]-1}}
\text{else if }\ \text{Region}= 5
\text{else if }\ \text{Region}= 5
Equations in LaTeX code
\text{else if }\ \text{Region}= 5
γ^r_{πτ}=\sum_{i=1}^{6}{n[i]\cdot I[i]\cdot π^{I[i]-1}\cdot J[i]\cdot τ^{J[i]-1}}
γ^r_{πτ}=\sum_{i=1}^{6}{n[i]\cdot I[i]\cdot π^{I[i]-1}\cdot J[i]\cdot τ^{J[i]-1}}
Equations in LaTeX code
γ^r_{πτ}=\sum_{i=1}^{6}{n[i]\cdot I[i]\cdot π^{I[i]-1}\cdot J[i]\cdot τ^{J[i]-1}}
\text{else}
\text{else}
Equations in LaTeX code
\text{else}
γ^r_{πτ}=0
γ^r_{πτ}=0
Equations in LaTeX code
γ^r_{πτ}=0
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