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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...

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...

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...

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...

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

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

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...

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,...

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

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

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