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 …

\displaystyle \text {tanh} (x + k\pi i) = \text {tanh}\ x tanh(x+kπi) = tanh x \displaystyle \text {coth} (x + k\pi i) =\text {coth} x coth(x+kπi) = cothx Relationship between inverse hyperbolic and …

5 days ago · The hyperbolic cotangent is defined as cothz= (e^z+e^ (-z))/ (e^z-e^ (-z))= (e^ (2z)+1)/ (e^ (2z)-1). (1) The notation cthz is sometimes also used (Gradshteyn and Ryzhik …

coth (z) = i cot (iz)

gives the hyperbolic cotangent of z. Mathematical function, suitable for both symbolic and numerical manipulation. automatically evaluates to exact values when its argument is the …

Here is a graphic of the hyperbolic cotangent function for real values of its argument . The hyperbolic cotangent function can be represented using more general mathematical functions.

Theorem Let z ∈ C z ∈ C be a complex number. Then: coth z = − cot(iz) coth ⁡ z = − cot ⁡ (i z) where: cot cot denotes the cotangent function coth coth denotes the hyperbolic cotangent i i is …

Coth [z] (840 formulas) Primary definition (1 formula) Specific values (88 formulas) General characteristics (9 formulas) Series representations (27 formulas) Integral representations (2 …

The real hyperbolic cotangent function is defined on the real numbers as: coth: R≠0 → R coth: R ≠ 0 → R: ∀x ∈ R≠0: coth x:= ex +e−x ex −e−x ∀ x ∈ R ≠ 0: coth ⁡ x:= e x + e − x e x − e − x …

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