sinh 双曲正弦，cosh 双曲余弦，tanh 双曲正切， sech 双曲正割，csch(cosech) 双曲余割，coth 双曲余切. 接下去是各个双曲函数的表达式： 来自网络 二、函数图像. 下面是各个双曲函数的图像以及对应定义域、值域等： y=\sinh x=\frac{e^x-e^{-x}}{2} y=sinh x. 2.

In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle.Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola.Also, similarly to how the derivatives of sin(t) and cos(t) are cos(t) and –sin(t) respectively, the ...

该页面介绍了双曲函数与反双曲函数的一些公式。

Inverse hyperbolic functions. If x = sinh y, then y = sinh-1 a is called the inverse hyperbolic sine of x. Similarly we define the other inverse hyperbolic functions. The inverse hyperbolic functions are multiple-valued and as in the case of inverse trigonometric functions we restrict ourselves to principal values for which they can be considered as single-valued.

Coth is the hyperbolic cotangent function, which is the hyperbolic analogue of the Cot circular function used throughout trigonometry. Coth [α] is defined as the ratio of the corresponding hyperbolic cosine and hyperbolic sine functions via . Coth may also be defined as , where is the base of the natural logarithm Log.; Coth automatically evaluates to exact values when its argument is the ...

双曲三角函数与三角函数是数学上最为常见的运算公式，这篇文章主要讲述一些关于双曲三角函数以及三角函数的泰勒展开式。 双曲三角函数,我们由定义很容易知道 \sinh{x},\cosh{x} 的展开式: \sinh{x}=\frac{e^{n}-e^…

在数学中，双曲函数是一类与常见的三角函数（也叫圆函数）类似的函数。最基本的双曲函数是双曲正弦函数sinh和双曲余弦函数cosh，从它们可以导出双曲正切函数tanh等，其推导也类似于三角函数的推导。双曲函数的反函数称为反双曲函数。双曲函数的定义域是区间，其自变量的值叫做双 …

2025年4月3日 · The hyperbolic cotangent satisfies the identity coth(z/2)-cothz=cschz, (2) where cschz is the hyperbolic cosecant. It has a unique real fixed point where cothu=u (3) at u^*=1.19967874... (OEIS A085984), which is related to the Laplace limit in the...

有 \displaystyle\sinh z=z\prod_{n=1}^{\infty}\left(1+\frac{z^{2}}{n^{2}\pi^{2}}\right). 取对数，求导，得 \displaystyle\coth z-\frac{1}{z}=\sum_{n=1}^{\infty ...

The hyperbolic cotangent of z in Math. Defined by \[ \coth z = \frac{ \cosh z }{ \sinh z } \] Real part on the real axis: Imaginary part on the real axis is zero. Real part on the imaginary axis is zero. Imaginary part on the imaginary axis: Real part on the complex plane: