\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\left(\left(1 - z\right) - 1\right) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]

\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\color{red}{\left(\left(1 - z\right) - 1\right)} + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right) \leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\color{blue}{\log_* (1 + (e^{\left(1 - z\right) - 1} - 1)^*)} + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right)\]

\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\log_* (1 + (e^{\left(1 - z\right) - 1} - 1)^*) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\left(\left(1 - z\right) - 1\right) + 8}\right)\right) \leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\log_* (1 + (e^{\left(1 - z\right) - 1} - 1)^*) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{-1 \cdot z + 8}\right)\right)\]

\[\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\log_* (1 + (e^{\left(1 - z\right) - 1} - 1)^*) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\color{red}{-1 \cdot z} + 8}\right)\right) \leadsto \frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\log_* (1 + (e^{\left(1 - z\right) - 1} - 1)^*) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{\color{blue}{-1 \cdot z} + 8}\right)\right)\]

\[\color{red}{\frac{\pi}{\sin \left(\pi \cdot z\right)} \cdot \left(\left(\left(\sqrt{\pi \cdot 2} \cdot {\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}^{\left(\left(\left(1 - z\right) - 1\right) + 0.5\right)}\right) \cdot e^{-\left(\left(\left(\left(1 - z\right) - 1\right) + 7\right) + 0.5\right)}\right) \cdot \left(\left(\left(\left(\left(\left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{\left(\left(1 - z\right) - 1\right) + 1}\right) + \frac{-1259.1392167224028}{\left(\left(1 - z\right) - 1\right) + 2}\right) + \frac{771.3234287776531}{\left(\left(1 - z\right) - 1\right) + 3}\right) + \frac{-176.6150291621406}{\left(\left(1 - z\right) - 1\right) + 4}\right) + \frac{12.507343278686905}{\left(\left(1 - z\right) - 1\right) + 5}\right) + \frac{-0.13857109526572012}{\log_* (1 + (e^{\left(1 - z\right) - 1} - 1)^*) + 6}\right) + \frac{9.984369578019572 \cdot 10^{-06}}{\left(\left(1 - z\right) - 1\right) + 7}\right) + \frac{1.5056327351493116 \cdot 10^{-07}}{-1 \cdot z + 8}\right)\right)} \leadsto \color{blue}{\left(\frac{{\left(\left(0.5 + 7\right) + \left(\left(1 - z\right) - 1\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{e^{\left(0.5 + 7\right) + \left(\left(1 - z\right) - 1\right)}} \cdot \frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{(z * -1 + 8)_*} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)} + \frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)\right) + \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - \left(z + 0\right)}\right) + \left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right)\right)\right)}\]

\[\left(\frac{{\left(\left(0.5 + 7\right) + \left(\left(1 - z\right) - 1\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{\color{red}{e^{\left(0.5 + 7\right) + \left(\left(1 - z\right) - 1\right)}}} \cdot \frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{(z * -1 + 8)_*} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)} + \frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)\right) + \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - \left(z + 0\right)}\right) + \left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right)\right)\right) \leadsto \left(\frac{{\left(\left(0.5 + 7\right) + \left(\left(1 - z\right) - 1\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}{\color{blue}{{\left(\sqrt[3]{e^{\left(0.5 + 7\right) + \left(\left(1 - z\right) - 1\right)}}\right)}^3}} \cdot \frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{(z * -1 + 8)_*} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)} + \frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)\right) + \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - \left(z + 0\right)}\right) + \left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right)\right)\right)\]

\[\left(\frac{\color{red}{{\left(\left(0.5 + 7\right) + \left(\left(1 - z\right) - 1\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}}{{\left(\sqrt[3]{e^{\left(0.5 + 7\right) + \left(\left(1 - z\right) - 1\right)}}\right)}^3} \cdot \frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{(z * -1 + 8)_*} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)} + \frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)\right) + \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - \left(z + 0\right)}\right) + \left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right)\right)\right) \leadsto \left(\frac{\color{blue}{{\left(\sqrt[3]{{\left(\left(0.5 + 7\right) + \left(\left(1 - z\right) - 1\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}\right)}^3}}{{\left(\sqrt[3]{e^{\left(0.5 + 7\right) + \left(\left(1 - z\right) - 1\right)}}\right)}^3} \cdot \frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{(z * -1 + 8)_*} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)} + \frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)\right) + \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - \left(z + 0\right)}\right) + \left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right)\right)\right)\]

\[\left(\color{red}{\frac{{\left(\sqrt[3]{{\left(\left(0.5 + 7\right) + \left(\left(1 - z\right) - 1\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}\right)}^3}{{\left(\sqrt[3]{e^{\left(0.5 + 7\right) + \left(\left(1 - z\right) - 1\right)}}\right)}^3}} \cdot \frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{(z * -1 + 8)_*} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)} + \frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)\right) + \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - \left(z + 0\right)}\right) + \left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right)\right)\right) \leadsto \left(\color{blue}{{\left(\frac{\sqrt[3]{{\left(\left(0.5 + 7\right) + \left(\left(1 - z\right) - 1\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}}{\sqrt[3]{e^{\left(0.5 + 7\right) + \left(\left(1 - z\right) - 1\right)}}}\right)}^3} \cdot \frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{(z * -1 + 8)_*} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)} + \frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)\right) + \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - \left(z + 0\right)}\right) + \left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right)\right)\right)\]

\[\left({\color{red}{\left(\frac{\sqrt[3]{{\left(\left(0.5 + 7\right) + \left(\left(1 - z\right) - 1\right)\right)}^{\left(\left(1 + 0.5\right) - \left(1 + z\right)\right)}}}{\sqrt[3]{e^{\left(0.5 + 7\right) + \left(\left(1 - z\right) - 1\right)}}}\right)}}^3 \cdot \frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{(z * -1 + 8)_*} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)} + \frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)\right) + \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - \left(z + 0\right)}\right) + \left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right)\right)\right) \leadsto \left({\color{blue}{\left(\frac{\sqrt[3]{{\left(7 + \left(0.5 - z\right)\right)}^{\left(0.5 - z\right)}}}{\sqrt[3]{e^{7 + \left(0.5 - z\right)}}}\right)}}^3 \cdot \frac{\pi \cdot \sqrt{\pi \cdot 2}}{\sin \left(z \cdot \pi\right)}\right) \cdot \left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{(z * -1 + 8)_*} + \left(\frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)} + \frac{-0.13857109526572012}{\left(1 - z\right) - \left(1 - 6\right)}\right)\right) + \left(\left(\left(0.9999999999998099 + \frac{676.5203681218851}{1 - \left(z + 0\right)}\right) + \left(\frac{771.3234287776531}{\left(1 - z\right) - \left(1 - 3\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right)\right) + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right)\right)\right)\]