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hyperbolic function


from The American Heritage® Dictionary of the English Language, 4th Edition

  • n. Any of a set of six functions related, for a real or complex variable x, to the hyperbola in a manner analogous to the relationship of the trigonometric functions to a circle, including:
  • n. The hyperbolic sine, defined by the equation sinh x = 1/2 (ex - e-x).
  • n. The hyperbolic cosine, defined by the equation cosh x = 1/2 (ex + e-x).
  • n. The hyperbolic tangent, defined by the equation tanh x = sinh x/cosh x.
  • n. The hyperbolic cotangent, defined by the equation coth x = cosh x/sinh x.
  • n. The hyperbolic secant, defined by the equation sech x = 1/cosh x.
  • n. The hyperbolic cosecant, defined by the equation csch x = 1/sinh x.

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. A function that is derived from some arithmetic operations on the exponential function with base e and the inverse function, and was named after the corresponding similar trigonometric function.


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