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...

{\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...

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

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...

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...

circular function Hyperbolic geometric graph, a random network generated by connecting nearby points sprinkled in a hyperbolic space Hyperbolic geometry...

hyperbola (/haɪˈpɜːrbələ/ ; pl. hyperbolas or hyperbolae /-liː/ ; adj. hyperbolic /ˌhaɪpərˈbɒlɪk/ ) is a type of smooth curve lying in a plane, defined...

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

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

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

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...

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

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

In mathematics, a hyperbolic partial differential equation of order n {\displaystyle n} is a partial differential equation (PDE) that, roughly speaking...

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

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

&{\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...

e^{x}=\cosh x+\sinh x.} These transcendental hyperbolic functions can be converted into circular functions sine and cosine by introducing (−1)k into the...

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

rules for computing the derivative of a function in calculus. Unless otherwise stated, all functions are functions of real numbers (R) that return real values;...

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

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

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...

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

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

even number of hyperbolic sines. The Gudermannian function gives a direct relationship between the trigonometric functions and the hyperbolic ones that does...

constant Gaussian curvature of the plane is −1. Sinh, cosh and tanh are hyperbolic functions. The polar coordinate system is a two-dimensional coordinate system...