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

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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 with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola.

Jan 18, 2015 · Remove the singularity by expanding cothx − 1 / x instead. There is a simple way of approximating coth by noticing that it is a logarithmic derivative.

In mathematics, the inverse hyperbolic functions are inverses of the hyperbolic functions, analogous to the inverse circular functions. There are six in common use: inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent, inverse hyperbolic cosecant, inverse hyperbolic secant, and inverse hyperbolic cotangent.

Illustrated definition of Coth: The Hyperbolic Cotangent Function. coth(x) (esupxsup esupminusxsup) (esupxsup minus...

coth (z) = i cot (iz)

Taylor series expansions of hyperbolic functions, i.e., sinh, cosh, tanh, coth, sech, and csch.

The domain restrictions for the inverse hyperbolic tangent and cotangent follow from the range of the functions \(y = \tanh x\) and \(y = \coth x,\) respectively. We also derive the derivatives of the inverse hyperbolic secant and cosecant , though these functions are rare.

La siguiente lista muestra los valores principales [a menos que se indique lo contrario] de las funciones hiperbólicas inversas expresadas en términos de funciones logarítmicas que se toman como valores reales.