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

\[\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}}{\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}}{-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}{\left(\left(1 - z\right) - 1\right) + 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}{\left(\left(1 - z\right) - 1\right) + 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)\]

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

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

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

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

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

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