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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 …

tanh(nx) = e2nx − 1 e2nx + 1 = 1 −e−2nx 1 +e−2nx. Use the second form and note that we have a clear difference here.... assuming n is not a function of x we have an exponential, which …

tanh(x) = sinh(x)/cosh(x) = ( e x - e-x)/( e x + e-x) coth(x) = 1/tanh(x) = ( e x + e-x)/( e x - e-x) cosh 2 (x) - sinh 2 (x) = 1 tanh 2 (x) + sech 2 (x) = 1 coth 2 (x) - csch 2 (x) = 1 Inverse Hyperbolic …

Let $n\in \mathbb{N}$. Please check if my reasoning is right: $\tanh (nx)=\frac{1-\exp(-2nx)}{1+\exp(2nx)}$ $\exp(x)$ ist uniform convergent on $\mathbb{R}$. Therefore $\tanh (nx)$ …

$\text{tanh} (x + k\pi i) = \text{tanh}\ x$ $\text{coth} (x + k\pi i) =\text{coth} x$ Relationship between inverse hyperbolic and inverse trigonometric functions

Tanh is the hyperbolic tangent function, which is the hyperbolic analogue of the Tan circular function used throughout trigonometry. Tanh [α] is defined as the ratio of the corresponding …

The first claim is false, in fact $\tanh nx \to \mathrm{sgn} x$ pointwise (with $\mathrm{sgn}(0) := 0$). Since $\tanh nx$ is continuous for all $n$ and $\mathrm{sgn}$ is not, the convergence …

Apr 16, 2008 · This paper presents a novel non-linear neural activation function architecture that approximates the tanh (nx) function accurately. The purpose of this realization is the …

This tanh calculator efficiently computes and clearly explains the hyperbolic tangent function.