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  2. Hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_functions

    The Gudermannian function gives a direct relationship between the circular functions and the hyperbolic functions that does not involve complex numbers. The graph of the function a cosh( x / a ) is the catenary , the curve formed by a uniform flexible chain, hanging freely between two fixed points under uniform gravity.

  3. List of integrals of hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    The following is a list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals. In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration.

  4. Hyperbolastic functions - Wikipedia

    en.wikipedia.org/wiki/Hyperbolastic_functions

    The hyperbolastic rate equation of type II, denoted by H2, is defined as = ⁡ (() ()),where is the hyperbolic tangent function, is the carrying capacity, and both and > jointly determine the growth rate.

  5. Inverse hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Inverse_hyperbolic_functions

    The argument to the hyperbolic functions is a hyperbolic angle measure. In mathematics, the inverse hyperbolic functions are inverses of the hyperbolic functions, analogous to the inverse circular functions. There are six in common use: inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent, inverse hyperbolic cosecant ...

  6. Hyperbola - Wikipedia

    en.wikipedia.org/wiki/Hyperbola

    Many other mathematical objects have their origin in the hyperbola, such as hyperbolic paraboloids (saddle surfaces), hyperboloids ("wastebaskets"), hyperbolic geometry (Lobachevsky's celebrated non-Euclidean geometry), hyperbolic functions (sinh, cosh, tanh, etc.), and gyrovector spaces (a geometry proposed for use in both relativity and ...

  7. List of integrals of inverse hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    The following is a list of indefinite integrals (antiderivatives) of expressions involving the inverse hyperbolic functions. For a complete list of integral formulas, see lists of integrals. In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration.

  8. Category:Hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Category:Hyperbolic_functions

    Pages in category "Hyperbolic functions" The following 25 pages are in this category, out of 25 total. This list may not reflect recent changes. ...

  9. Coordinate systems for the hyperbolic plane - Wikipedia

    en.wikipedia.org/wiki/Coordinate_systems_for_the...

    Several qualitatively different ways of coordinatizing the plane in hyperbolic geometry are used. This article tries to give an overview of several coordinate systems in use for the two-dimensional hyperbolic plane. In the descriptions below the constant Gaussian curvature of the plane is −1. Sinh, cosh and tanh are hyperbolic functions.

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