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

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

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