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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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