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...

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...

{\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...

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...

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...

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

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...

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

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 )...

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

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...

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...

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

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

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...

functions and their inverses in terms of the exponential function and the complex logarithm. Trigonometric functions may be deduced from 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 mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum, as...

derivative of a constant function is 0. Inverse hyperbolic functions over the complex domain are multiple-valued because hyperbolic functions are periodic along...