[求助] 一个函数的定积分求解

2楼: Originally posted by alober at 2017-02-21 16:00:29
f(t)=\int_{0}^{\sqrt{t}}(x^2-1)^{-\frac{1}{4}}dx
f(t) \mathop{=}^{x^2=y} \frac{(-1)^{-\frac{1}{4}}}{2}\int_{0}^{t}y^{-\frac{1}{2}}(1-y)^{-\frac{1}{4}}dy \mathop{=}^{y=tx} \frac{(-1)^{-\frac{1}{4}}}{ ...

2楼: Originally posted by alober at 2017-02-21 16:00:29
f(t)=\int_{0}^{\sqrt{t}}(x^2-1)^{-\frac{1}{4}}dx
f(t) \mathop{=}^{x^2=y} \frac{(-1)^{-\frac{1}{4}}}{2}\int_{0}^{t}y^{-\frac{1}{2}}(1-y)^{-\frac{1}{4}}dy \mathop{=}^{y=tx} \frac{(-1)^{-\frac{1}{4}}}{ ...

3楼: Originally posted by xiaojixiong at 2017-02-22 15:28:16
非常感谢您的热心帮助！能不能给出f(t)倒数第二步的标准积分表啊？还有就是F1是个啥函数。然后这个破积分我找到原始出处了。.
参考文献：H. R. JORY and A. W. TRIVELPIECE. Exact relativistic solution for t ...