In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just...

mathematics, the inverse hyperbolic functions are inverses of the hyperbolic functions, analogous to the inverse circular functions. There are six in common...

{gd} \psi } . The Gudermannian function reveals a close relationship between the circular functions and hyperbolic functions. It was introduced in the 1760s...

{\sqrt {2}}} . Hyperbolic angle is used as the independent variable for the hyperbolic functions sinh, cosh, and tanh, because these functions may be premised...

hyperbolic sector in standard position has a = 1 and b > 1. Hyperbolic sectors are the basis for the hyperbolic functions. The area of a hyperbolic sector...

to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of α {\displaystyle \alpha...

second word of دالة زائدية "hyperbolic function") is added to the end of trigonometric functions to express hyperbolic functions. This is similar to the way...

List of integrals of hyperbolic functions List of integrals of inverse hyperbolic functions List of integrals of exponential functions List of integrals...

hyperbolic geometry (Lobachevsky's celebrated non-Euclidean geometry), hyperbolic functions (sinh, cosh, tanh, etc.), and gyrovector spaces (a geometry proposed...

algebraic function. Examples of transcendental functions include the exponential function, the logarithm function, the hyperbolic functions, and the trigonometric...

rational, trigonometric, hyperbolic, and exponential functions, and their inverses (e.g., arcsin, log, or x1/n). All elementary functions are continuous on their...

list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals. In all formulas...

Transcendental functions are functions that are not algebraic. Exponential function: raises a fixed number to a variable power. Hyperbolic functions: formally...

integrals are a family of nonelementary integrals involving trigonometric functions. The different sine integral definitions are Si ⁡ ( x ) = ∫ 0 x sin ⁡...

Euler numbers. The hyperbolic functions have Maclaurin series closely related to the series for the corresponding trigonometric functions: sinh ⁡ x = ∑ n...

simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots, multiplications, divisions, and exponentials...

hyperbolic tangent, also known as (parametric) Soboleva modified hyperbolic tangent activation function ([P]SMHTAF), is a special S-shaped function based...

trigonometric functions has a corresponding inverse function, and an analog among the hyperbolic functions. The oldest definitions of trigonometric functions, related...

plane in mathematics Hyperbolic geometry, a non-Euclidean geometry Hyperbolic functions, analogues of ordinary trigonometric functions, defined using the...

stock splits versus stock buy-back. The hyperbolic functions sinh, cosh, and tanh can be illustrated with hyperbolic coordinates. Let A = ( e t , e − t )...

the theory of hyperbolic functions and, indeed, our present notation for these functions. Ratcliffe, John (2006), Foundations of Hyperbolic Manifolds, Graduate...

infinite series of any rational function of n {\displaystyle n} can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition...

rules for computing the derivative of a function in calculus. Unless otherwise stated, all functions are functions of real numbers ( R {\textstyle \mathbb...

is an acronym for "Cos i Sin". It connects trigonometric functions with exponential functions in the complex plane via Euler's formula. While the domain...

functions we have a function from angles to slopes. As with other properties shared between the trigonometric functions and the hyperbolic functions,...

there is a corresponding formula in the list of integrals of inverse hyperbolic functions. ∫ arcsin ⁡ ( x ) d x = x arcsin ⁡ ( x ) + 1 − x 2 + C {\displaystyle...

function is typically called the arcsine function, written as arcsin(x). Similarly, the inverse of a hyperbolic function is indicated by the prefix "ar" (for...

trigonometric functions (occasionally also called antitrigonometric, cyclometric, or arcus functions) are the inverse functions of the trigonometric functions, under...

Indefinite sum Gamma function List of limits Reynolds, Robert; Stauffer, Allan (2020). "Derivation of Logarithmic and Logarithmic Hyperbolic Tangent Integrals...

transformation groups. The hyperbolic functions, which take hyperbolic angle as argument, perform the role that circular functions play with the circular...