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

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

\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{(z * -1 + 8)_*} + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right)\right) + \left(\left(\frac{771.3234287776531}{\left(1 + 3\right) - \left(1 + z\right)} + \frac{-1259.1392167224028}{\left(1 - z\right) - \left(1 - 2\right)}\right) + \left(0.9999999999998099 + \frac{676.5203681218851}{1 - \left(z + 0\right)}\right)\right)\right) + \left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right)\right) \cdot \frac{\left(\sqrt{\pi \cdot 2} \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right) \cdot {\left(\left(\left(1 - z\right) - \left(1 - 7\right)\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{\left(\left(1 - z\right) - \left(1 - 7\right)\right) + 0.5}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{(z * -1 + 8)_*} + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right)\right) + \left(447.4381671388014 \cdot z + \left(305.05856935323453 + 547.6955004307571 \cdot {z}^2\right)\right)\right) + \left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right)\right) \cdot \frac{\left(\sqrt{\pi \cdot 2} \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right) \cdot {\left(\left(\left(1 - z\right) - \left(1 - 7\right)\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{\left(\left(1 - z\right) - \left(1 - 7\right)\right) + 0.5}}\]

\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{(z * -1 + 8)_*} + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right)\right) + \color{red}{\left(447.4381671388014 \cdot z + \left(305.05856935323453 + 547.6955004307571 \cdot {z}^2\right)\right)}\right) + \left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right)\right) \cdot \frac{\left(\sqrt{\pi \cdot 2} \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right) \cdot {\left(\left(\left(1 - z\right) - \left(1 - 7\right)\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{\left(\left(1 - z\right) - \left(1 - 7\right)\right) + 0.5}} \leadsto \left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{(z * -1 + 8)_*} + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right)\right) + \color{blue}{\left(447.4381671388014 \cdot z + \left(305.05856935323453 + 547.6955004307571 \cdot {z}^2\right)\right)}\right) + \left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right)\right) \cdot \frac{\left(\sqrt{\pi \cdot 2} \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right) \cdot {\left(\left(\left(1 - z\right) - \left(1 - 7\right)\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{\left(\left(1 - z\right) - \left(1 - 7\right)\right) + 0.5}}\]

\[\left(\left(\left(\frac{1.5056327351493116 \cdot 10^{-07}}{(z * -1 + 8)_*} + \left(\frac{-176.6150291621406}{\left(4 + 1\right) - \left(1 + z\right)} + \frac{12.507343278686905}{\left(1 - z\right) - \left(1 - 5\right)}\right)\right) + \left(447.4381671388014 \cdot z + \left(305.05856935323453 + 547.6955004307571 \cdot {z}^2\right)\right)\right) + \left(\frac{-0.13857109526572012}{\left(6 + 1\right) - \left(1 + z\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{\left(1 - z\right) - \left(1 - 7\right)}\right)\right) \cdot \frac{\left(\sqrt{\pi \cdot 2} \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}\right) \cdot {\left(\left(\left(1 - z\right) - \left(1 - 7\right)\right) + 0.5\right)}^{\left(\left(1 - z\right) - \left(1 - 0.5\right)\right)}}{e^{\left(\left(1 - z\right) - \left(1 - 7\right)\right) + 0.5}} \leadsto \frac{\frac{\pi}{\frac{\sin \left(z \cdot \pi\right)}{\sqrt{2 \cdot \pi}}}}{\frac{e^{\left(0 - z\right) + \left(7 + 0.5\right)}}{{\left(\left(0 - z\right) + \left(7 + 0.5\right)\right)}^{\left(0.5 + \left(0 - z\right)\right)}}} \cdot \left(\left(\left(\frac{-176.6150291621406}{\left(4 + 0\right) - z} + \frac{1.5056327351493116 \cdot 10^{-07}}{(z * -1 + 8)_*}\right) + \left(\frac{12.507343278686905}{5 + \left(0 - z\right)} + (\left(z \cdot z\right) * 547.6955004307571 + \left((z * 447.4381671388014 + 305.05856935323453)_*\right))_*\right)\right) + \left(\frac{-0.13857109526572012}{6 + \left(0 - z\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(0 - z\right)}\right)\right)\]

\[\color{red}{\frac{\frac{\pi}{\frac{\sin \left(z \cdot \pi\right)}{\sqrt{2 \cdot \pi}}}}{\frac{e^{\left(0 - z\right) + \left(7 + 0.5\right)}}{{\left(\left(0 - z\right) + \left(7 + 0.5\right)\right)}^{\left(0.5 + \left(0 - z\right)\right)}}} \cdot \left(\left(\left(\frac{-176.6150291621406}{\left(4 + 0\right) - z} + \frac{1.5056327351493116 \cdot 10^{-07}}{(z * -1 + 8)_*}\right) + \left(\frac{12.507343278686905}{5 + \left(0 - z\right)} + (\left(z \cdot z\right) * 547.6955004307571 + \left((z * 447.4381671388014 + 305.05856935323453)_*\right))_*\right)\right) + \left(\frac{-0.13857109526572012}{6 + \left(0 - z\right)} + \frac{9.984369578019572 \cdot 10^{-06}}{7 + \left(0 - z\right)}\right)\right)} \leadsto \color{blue}{\left(\left(\left(\frac{-176.6150291621406}{4 - z} + \frac{1.5056327351493116 \cdot 10^{-07}}{(z * -1 + 8)_*}\right) + \left((\left(z \cdot z\right) * 547.6955004307571 + \left((z * 447.4381671388014 + 305.05856935323453)_*\right))_* + \frac{12.507343278686905}{5 - z}\right)\right) + \left(\frac{-0.13857109526572012}{6 - z} + \frac{9.984369578019572 \cdot 10^{-06}}{7 - z}\right)\right) \cdot \frac{\sqrt{\pi \cdot 2} \cdot \frac{\pi}{\sin \left(z \cdot \pi\right)}}{\frac{e^{7 + \left(0.5 - z\right)}}{{\left(7 + \left(0.5 - z\right)\right)}^{\left(0.5 - z\right)}}}}\]