if alpha < 7.711586793570146e+139

1. Started with
   \[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}\]
   49.6
2. Applied simplify to get
   \[\color{red}{\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}} \leadsto \color{blue}{\frac{\left(\frac{\left(\beta + \alpha\right) + i}{\beta + (i * 2 + \alpha)_*} \cdot (i * \left(\left(\beta + \alpha\right) + i\right) + \left(\alpha \cdot \beta\right))_*\right) \cdot \frac{i}{\beta + (i * 2 + \alpha)_*}}{{\left(\beta + (i * 2 + \alpha)_*\right)}^2 - 1.0}}\]
   34.7
3. Applied taylor to get
   \[\frac{\left(\frac{\left(\beta + \alpha\right) + i}{\beta + (i * 2 + \alpha)_*} \cdot (i * \left(\left(\beta + \alpha\right) + i\right) + \left(\alpha \cdot \beta\right))_*\right) \cdot \frac{i}{\beta + (i * 2 + \alpha)_*}}{{\left(\beta + (i * 2 + \alpha)_*\right)}^2 - 1.0} \leadsto \frac{\left(\frac{\left(\beta + \alpha\right) + i}{\beta + (i * 2 + \alpha)_*} \cdot (i * \left(\left(\beta + \alpha\right) + i\right) + \left(\alpha \cdot \beta\right))_*\right) \cdot \frac{i}{\beta + (i * 2 + \alpha)_*}}{\left(2 \cdot \left(\beta \cdot (i * 2 + \alpha)_*\right) + \left({\left((i * 2 + \alpha)_*\right)}^2 + {\beta}^2\right)\right) - 1.0}\]
   34.7
4. Taylor expanded around 0 to get
   \[\frac{\left(\frac{\left(\beta + \alpha\right) + i}{\beta + (i * 2 + \alpha)_*} \cdot (i * \left(\left(\beta + \alpha\right) + i\right) + \left(\alpha \cdot \beta\right))_*\right) \cdot \frac{i}{\beta + (i * 2 + \alpha)_*}}{\color{red}{\left(2 \cdot \left(\beta \cdot (i * 2 + \alpha)_*\right) + \left({\left((i * 2 + \alpha)_*\right)}^2 + {\beta}^2\right)\right)} - 1.0} \leadsto \frac{\left(\frac{\left(\beta + \alpha\right) + i}{\beta + (i * 2 + \alpha)_*} \cdot (i * \left(\left(\beta + \alpha\right) + i\right) + \left(\alpha \cdot \beta\right))_*\right) \cdot \frac{i}{\beta + (i * 2 + \alpha)_*}}{\color{blue}{\left(2 \cdot \left(\beta \cdot (i * 2 + \alpha)_*\right) + \left({\left((i * 2 + \alpha)_*\right)}^2 + {\beta}^2\right)\right)} - 1.0}\]
   34.7
5. Applied simplify to get
   \[\color{red}{\frac{\left(\frac{\left(\beta + \alpha\right) + i}{\beta + (i * 2 + \alpha)_*} \cdot (i * \left(\left(\beta + \alpha\right) + i\right) + \left(\alpha \cdot \beta\right))_*\right) \cdot \frac{i}{\beta + (i * 2 + \alpha)_*}}{\left(2 \cdot \left(\beta \cdot (i * 2 + \alpha)_*\right) + \left({\left((i * 2 + \alpha)_*\right)}^2 + {\beta}^2\right)\right) - 1.0}} \leadsto \color{blue}{\frac{\frac{i}{(i * 2 + \alpha)_* + \beta} \cdot \frac{\left(\alpha + i\right) + \beta}{(i * 2 + \alpha)_* + \beta}}{\frac{(\left((i * 2 + \alpha)_*\right) * \left((\beta * 2 + \left((i * 2 + \alpha)_*\right))_*\right) + \left({\beta}^2 - 1.0\right))_*}{(i * \left(\left(\alpha + i\right) + \beta\right) + \left(\alpha \cdot \beta\right))_*}}}\]
   34.7
6. Using strategy rm
   34.7
7. Applied add-sqr-sqrt to get
   \[\frac{\frac{i}{(i * 2 + \alpha)_* + \beta} \cdot \frac{\left(\alpha + i\right) + \beta}{(i * 2 + \alpha)_* + \beta}}{\color{red}{\frac{(\left((i * 2 + \alpha)_*\right) * \left((\beta * 2 + \left((i * 2 + \alpha)_*\right))_*\right) + \left({\beta}^2 - 1.0\right))_*}{(i * \left(\left(\alpha + i\right) + \beta\right) + \left(\alpha \cdot \beta\right))_*}}} \leadsto \frac{\frac{i}{(i * 2 + \alpha)_* + \beta} \cdot \frac{\left(\alpha + i\right) + \beta}{(i * 2 + \alpha)_* + \beta}}{\color{blue}{{\left(\sqrt{\frac{(\left((i * 2 + \alpha)_*\right) * \left((\beta * 2 + \left((i * 2 + \alpha)_*\right))_*\right) + \left({\beta}^2 - 1.0\right))_*}{(i * \left(\left(\alpha + i\right) + \beta\right) + \left(\alpha \cdot \beta\right))_*}}\right)}^2}}\]
   34.7

if 7.711586793570146e+139 < alpha

1. Started with
   \[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}\]
   63.0
2. Applied simplify to get
   \[\color{red}{\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}} \leadsto \color{blue}{\frac{\left(\frac{\left(\beta + \alpha\right) + i}{\beta + (i * 2 + \alpha)_*} \cdot (i * \left(\left(\beta + \alpha\right) + i\right) + \left(\alpha \cdot \beta\right))_*\right) \cdot \frac{i}{\beta + (i * 2 + \alpha)_*}}{{\left(\beta + (i * 2 + \alpha)_*\right)}^2 - 1.0}}\]
   56.7
3. Applied taylor to get
   \[\frac{\left(\frac{\left(\beta + \alpha\right) + i}{\beta + (i * 2 + \alpha)_*} \cdot (i * \left(\left(\beta + \alpha\right) + i\right) + \left(\alpha \cdot \beta\right))_*\right) \cdot \frac{i}{\beta + (i * 2 + \alpha)_*}}{{\left(\beta + (i * 2 + \alpha)_*\right)}^2 - 1.0} \leadsto \frac{\left(\frac{\left(\beta + \alpha\right) + i}{\beta + (i * 2 + \alpha)_*} \cdot (i * \left(\left(\beta + \alpha\right) + i\right) + \left(\alpha \cdot \beta\right))_*\right) \cdot \frac{i}{\beta + (i * 2 + \alpha)_*}}{\left(2 \cdot \left(\beta \cdot (i * 2 + \alpha)_*\right) + \left({\left((i * 2 + \alpha)_*\right)}^2 + {\beta}^2\right)\right) - 1.0}\]
   56.7
4. Taylor expanded around 0 to get
   \[\frac{\left(\frac{\left(\beta + \alpha\right) + i}{\beta + (i * 2 + \alpha)_*} \cdot (i * \left(\left(\beta + \alpha\right) + i\right) + \left(\alpha \cdot \beta\right))_*\right) \cdot \frac{i}{\beta + (i * 2 + \alpha)_*}}{\color{red}{\left(2 \cdot \left(\beta \cdot (i * 2 + \alpha)_*\right) + \left({\left((i * 2 + \alpha)_*\right)}^2 + {\beta}^2\right)\right)} - 1.0} \leadsto \frac{\left(\frac{\left(\beta + \alpha\right) + i}{\beta + (i * 2 + \alpha)_*} \cdot (i * \left(\left(\beta + \alpha\right) + i\right) + \left(\alpha \cdot \beta\right))_*\right) \cdot \frac{i}{\beta + (i * 2 + \alpha)_*}}{\color{blue}{\left(2 \cdot \left(\beta \cdot (i * 2 + \alpha)_*\right) + \left({\left((i * 2 + \alpha)_*\right)}^2 + {\beta}^2\right)\right)} - 1.0}\]
   56.7
5. Applied simplify to get
   \[\color{red}{\frac{\left(\frac{\left(\beta + \alpha\right) + i}{\beta + (i * 2 + \alpha)_*} \cdot (i * \left(\left(\beta + \alpha\right) + i\right) + \left(\alpha \cdot \beta\right))_*\right) \cdot \frac{i}{\beta + (i * 2 + \alpha)_*}}{\left(2 \cdot \left(\beta \cdot (i * 2 + \alpha)_*\right) + \left({\left((i * 2 + \alpha)_*\right)}^2 + {\beta}^2\right)\right) - 1.0}} \leadsto \color{blue}{\frac{\frac{i}{(i * 2 + \alpha)_* + \beta} \cdot \frac{\left(\alpha + i\right) + \beta}{(i * 2 + \alpha)_* + \beta}}{\frac{(\left((i * 2 + \alpha)_*\right) * \left((\beta * 2 + \left((i * 2 + \alpha)_*\right))_*\right) + \left({\beta}^2 - 1.0\right))_*}{(i * \left(\left(\alpha + i\right) + \beta\right) + \left(\alpha \cdot \beta\right))_*}}}\]
   56.7
6. Applied taylor to get
   \[\frac{\frac{i}{(i * 2 + \alpha)_* + \beta} \cdot \frac{\left(\alpha + i\right) + \beta}{(i * 2 + \alpha)_* + \beta}}{\frac{(\left((i * 2 + \alpha)_*\right) * \left((\beta * 2 + \left((i * 2 + \alpha)_*\right))_*\right) + \left({\beta}^2 - 1.0\right))_*}{(i * \left(\left(\alpha + i\right) + \beta\right) + \left(\alpha \cdot \beta\right))_*}} \leadsto \frac{\frac{i}{(i * 2 + \alpha)_* + \beta} \cdot \frac{\left(\alpha + i\right) + \beta}{(i * 2 + \alpha)_* + \beta}}{\frac{(\left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right) * \left((\left(\frac{1}{\beta}\right) * 2 + \left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right))_*\right) + \left(\frac{1}{{\beta}^2} - 1.0\right))_*}{(\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{\alpha} + \frac{1}{i}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_*}}\]
   3.4
7. Taylor expanded around inf to get
   \[\frac{\frac{i}{(i * 2 + \alpha)_* + \beta} \cdot \frac{\left(\alpha + i\right) + \beta}{(i * 2 + \alpha)_* + \beta}}{\color{red}{\frac{(\left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right) * \left((\left(\frac{1}{\beta}\right) * 2 + \left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right))_*\right) + \left(\frac{1}{{\beta}^2} - 1.0\right))_*}{(\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{\alpha} + \frac{1}{i}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_*}}} \leadsto \frac{\frac{i}{(i * 2 + \alpha)_* + \beta} \cdot \frac{\left(\alpha + i\right) + \beta}{(i * 2 + \alpha)_* + \beta}}{\color{blue}{\frac{(\left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right) * \left((\left(\frac{1}{\beta}\right) * 2 + \left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right))_*\right) + \left(\frac{1}{{\beta}^2} - 1.0\right))_*}{(\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{\alpha} + \frac{1}{i}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_*}}}\]
   3.4
8. Applied taylor to get
   \[\frac{\frac{i}{(i * 2 + \alpha)_* + \beta} \cdot \frac{\left(\alpha + i\right) + \beta}{(i * 2 + \alpha)_* + \beta}}{\frac{(\left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right) * \left((\left(\frac{1}{\beta}\right) * 2 + \left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right))_*\right) + \left(\frac{1}{{\beta}^2} - 1.0\right))_*}{(\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{\alpha} + \frac{1}{i}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_*}} \leadsto \frac{{i}^2 \cdot (\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{\alpha} + \frac{1}{i}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_*}{(\left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right) * \left((\left(\frac{1}{\beta}\right) * 2 + \left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right))_*\right) + \left(\frac{1}{{\beta}^2} - 1.0\right))_* \cdot {\left((i * 2 + \alpha)_*\right)}^2} + \left(\frac{\beta \cdot \left(i \cdot (\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{\alpha} + \frac{1}{i}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_*\right)}{(\left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right) * \left((\left(\frac{1}{\beta}\right) * 2 + \left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right))_*\right) + \left(\frac{1}{{\beta}^2} - 1.0\right))_* \cdot {\left((i * 2 + \alpha)_*\right)}^2} + \frac{\alpha \cdot \left(i \cdot (\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{\alpha} + \frac{1}{i}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_*\right)}{(\left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right) * \left((\left(\frac{1}{\beta}\right) * 2 + \left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right))_*\right) + \left(\frac{1}{{\beta}^2} - 1.0\right))_* \cdot {\left((i * 2 + \alpha)_*\right)}^2}\right)\]
   58.2
9. Taylor expanded around 0 to get
   \[\color{red}{\frac{{i}^2 \cdot (\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{\alpha} + \frac{1}{i}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_*}{(\left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right) * \left((\left(\frac{1}{\beta}\right) * 2 + \left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right))_*\right) + \left(\frac{1}{{\beta}^2} - 1.0\right))_* \cdot {\left((i * 2 + \alpha)_*\right)}^2} + \left(\frac{\beta \cdot \left(i \cdot (\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{\alpha} + \frac{1}{i}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_*\right)}{(\left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right) * \left((\left(\frac{1}{\beta}\right) * 2 + \left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right))_*\right) + \left(\frac{1}{{\beta}^2} - 1.0\right))_* \cdot {\left((i * 2 + \alpha)_*\right)}^2} + \frac{\alpha \cdot \left(i \cdot (\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{\alpha} + \frac{1}{i}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_*\right)}{(\left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right) * \left((\left(\frac{1}{\beta}\right) * 2 + \left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right))_*\right) + \left(\frac{1}{{\beta}^2} - 1.0\right))_* \cdot {\left((i * 2 + \alpha)_*\right)}^2}\right)} \leadsto \color{blue}{\frac{{i}^2 \cdot (\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{\alpha} + \frac{1}{i}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_*}{(\left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right) * \left((\left(\frac{1}{\beta}\right) * 2 + \left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right))_*\right) + \left(\frac{1}{{\beta}^2} - 1.0\right))_* \cdot {\left((i * 2 + \alpha)_*\right)}^2} + \left(\frac{\beta \cdot \left(i \cdot (\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{\alpha} + \frac{1}{i}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_*\right)}{(\left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right) * \left((\left(\frac{1}{\beta}\right) * 2 + \left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right))_*\right) + \left(\frac{1}{{\beta}^2} - 1.0\right))_* \cdot {\left((i * 2 + \alpha)_*\right)}^2} + \frac{\alpha \cdot \left(i \cdot (\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{\alpha} + \frac{1}{i}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_*\right)}{(\left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right) * \left((\left(\frac{1}{\beta}\right) * 2 + \left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right))_*\right) + \left(\frac{1}{{\beta}^2} - 1.0\right))_* \cdot {\left((i * 2 + \alpha)_*\right)}^2}\right)}\]
   58.2
10. Applied simplify to get
    \[\frac{{i}^2 \cdot (\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{\alpha} + \frac{1}{i}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_*}{(\left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right) * \left((\left(\frac{1}{\beta}\right) * 2 + \left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right))_*\right) + \left(\frac{1}{{\beta}^2} - 1.0\right))_* \cdot {\left((i * 2 + \alpha)_*\right)}^2} + \left(\frac{\beta \cdot \left(i \cdot (\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{\alpha} + \frac{1}{i}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_*\right)}{(\left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right) * \left((\left(\frac{1}{\beta}\right) * 2 + \left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right))_*\right) + \left(\frac{1}{{\beta}^2} - 1.0\right))_* \cdot {\left((i * 2 + \alpha)_*\right)}^2} + \frac{\alpha \cdot \left(i \cdot (\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{\alpha} + \frac{1}{i}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_*\right)}{(\left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right) * \left((\left(\frac{1}{\beta}\right) * 2 + \left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right))_*\right) + \left(\frac{1}{{\beta}^2} - 1.0\right))_* \cdot {\left((i * 2 + \alpha)_*\right)}^2}\right) \leadsto (\left(\frac{i}{(\left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right) * \left((\left(\frac{1}{\beta}\right) * 2 + \left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right))_*\right) + \left(\frac{\frac{1}{\beta}}{\beta} - 1.0\right))_*} \cdot \frac{i}{{\left((i * 2 + \alpha)_*\right)}^2}\right) * \left((\left(\frac{1}{i}\right) * \left(\left(\frac{1}{i} + \frac{1}{\alpha}\right) + \frac{1}{\beta}\right) + \left(\frac{\frac{1}{\beta}}{\alpha}\right))_*\right) + \left((\left(\frac{\beta}{(\left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right) * \left((\left(\frac{1}{\beta}\right) * 2 + \left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right))_*\right) + \left(\frac{\frac{1}{\beta}}{\beta} - 1.0\right))_*}\right) * \left(\frac{(\left(\frac{1}{i}\right) * \left(\left(\frac{1}{i} + \frac{1}{\alpha}\right) + \frac{1}{\beta}\right) + \left(\frac{\frac{1}{\beta}}{\alpha}\right))_*}{\frac{{\left((i * 2 + \alpha)_*\right)}^2}{i}}\right) + \left(\frac{\alpha}{(\left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right) * \left((\left(\frac{1}{\beta}\right) * 2 + \left((\left(\frac{1}{i}\right) * 2 + \left(\frac{1}{\alpha}\right))_*\right))_*\right) + \left(\frac{\frac{1}{\beta}}{\beta} - 1.0\right))_*} \cdot \frac{(\left(\frac{1}{i}\right) * \left(\left(\frac{1}{i} + \frac{1}{\alpha}\right) + \frac{1}{\beta}\right) + \left(\frac{\frac{1}{\beta}}{\alpha}\right))_*}{\frac{{\left((i * 2 + \alpha)_*\right)}^2}{i}}\right))_*\right))_*\]
    20.4

---

11. Applied final simplification