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  2. Inverse hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Inverse_hyperbolic_functions

    Following this recommendation, the ISO 80000-2 standard abbreviations use the prefix ar-(that is: arsinh, arcosh, artanh, arsech, arcsch, arcoth). In computer programming languages, inverse circular and hyperbolic functions are often named with the shorter prefix a-(asinh, etc.). This article will consistently adopt the prefix ar-for convenience.

  3. Hyperboloid model - Wikipedia

    en.wikipedia.org/wiki/Hyperboloid_model

    where arcosh is the inverse function of hyperbolic cosine. Choice of metric signature. The bilinear form also functions as the ...

  4. 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.

  5. Inverse trigonometric functions - Wikipedia

    en.wikipedia.org/.../Inverse_trigonometric_functions

    The absolute value in the argument of the arcosh function creates a negative half of its graph, making it identical to the signum logarithmic function shown above. All of these antiderivatives can be derived using integration by parts and the simple derivative forms shown above.

  6. Coordinate systems for the hyperbolic plane - Wikipedia

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

    The Poincaré half-plane model is closely related to a model of the hyperbolic plane in the quadrant Q = {(x,y): x > 0, y > 0}. For such a point the geometric mean = and the hyperbolic angle = ⁡ / produce a point (u,v) in the upper half-plane.

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  8. 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.

  9. Trading for DeAndre Hopkins showed Chiefs’ ability to balance ...

    www.aol.com/trading-deandre-hopkins-showed...

    Kansas City Chiefs players celebrated with Kansas City Chiefs wide receiver DeAndre Hopkins (8) after Hopkins made a catch for a touchdown in the second quarter against the Tampa Bay Buccaneers on ...