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...

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

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...

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

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

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

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

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

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

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

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

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...

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

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

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

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

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...

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

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

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

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;...

simplest case. The other cases are done in the same way. The utility of hyperbolic functions in integration can be demonstrated in cases of odd powers of secant...

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

&{\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...

In economics, hyperbolic discounting is a time-inconsistent model of delay discounting. It is one of the cornerstones of behavioral economics and its brain-basis...

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

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...