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\[\sum _{k=0}^{\infty } \binom{\frac{1}{2}}{k} \left(-\frac{1}{2}\right)^k=\left(1-\frac12\right)^{\frac12}\]
把 \binom 反过来:
\[\sum _{k=0}^{\infty } \binom{k}{\frac{1}{2}} \left(-\frac{1}{2}\right)^k=\frac{12+2\sqrt{3} \log \left(2- \sqrt{3}\right)}{9 \pi }\]
好像只有当$\frac12$能写成arcsinh的形式 |
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