Tanhc函数

Tanhc函数定义如下

${\displaystyle {\int <!--\; \int \; -->}_0^z\frac{\tanh <!--\; \; -->\left(x\right)}{x}dx}$

${\displaystyle tanhc\approx <!--\; \approx \; -->(1-<!--\; -\; -->\frac{1}{3}{z}^2+\frac{2}{15}{z}^4-<!--\; -\; -->\frac{17}{315}{z}^6+\frac{62}{2835}{z}^8-<!--\; -\; -->\frac{1382}{155925}{z}^{10}+\frac{21844}{6081075}{z}^{12}-<!--\; -\; -->\frac{929569}{638512875}{z}^{14}+O\left(z^{16}\right))}$

${\displaystyle {\int <!--\; \int \; -->}_0^z\frac{\tanh <!--\; \; -->\left(x\right)}{x}dx=(z-<!--\; -\; -->\frac{1}{9}{z}^3+\frac{2}{75}{z}^5-<!--\; -\; -->\frac{17}{2205}{z}^7+\frac{62}{25515}{z}^9-<!--\; -\; -->\frac{1382}{1715175}{z}^{11}+O\left(z^{13}\right))}$