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...

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...

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...

unit hyperbola. A hyperbolic sector in standard position has a = 1 and b > 1. The argument of hyperbolic functions is the hyperbolic angle, which is defined...

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

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

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

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

compositions of finitely many polynomial, rational, trigonometric, hyperbolic, and exponential functions, and their inverses (e.g., arcsin or log), as well as roots...

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

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

growth, hyperbolic growth is highly nonlinear, but differs in important respects. These functions can be confused, as exponential growth, hyperbolic growth...

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

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 ⁡...

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...

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

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

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

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

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

}}}}}}}}.} The inverse hyperbolic functions are related to the inverse trigonometric functions similar to how the hyperbolic functions are related to the...

everywhere, such as the exponential function, the sine and cosine functions, and the hyperbolic functions, but also to functions with branch cuts and poles, such...

trigonometric functions (arcsin, arccos, arctan, etc.) and inverse hyperbolic functions (arsinh, arcosh, artanh, etc.) can be defined in terms of logarithms...

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...

&{\text{if }}\eta =-1.\end{cases}}} The Bose distribution function is related to hyperbolic cotangent function by n B ( ξ ) = 1 2 ( coth ⁡ β ξ 2 − 1 ) . {\displaystyle...

integrals (antiderivatives) of expressions involving the inverse hyperbolic functions. For a complete list of integral formulas, see lists of integrals...