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In mathematics, the inverse hyperbolic functions provide a hyperbolic angle corresponding to a given value of a hyperbolic function. The size of the hyperbolic angle is equal to the area of the corresponding hyperbolic sector of the hyperbola , or twice the area of the corresponding sector of the unit hyperbola , just as a circular angle is twice the area of the circular sector of the unit circle. Some authors have called inverse hyperbolic functions "area functions" to realize the hyperbolic angles. ==Notation== The preferred abbreviations are ar- followed by the hyperbolic function (arsinh, arcosh, etc.). However, arc- followed by the hyperbolic function (for example arcsinh, arccosh), are also commonly seen by analogy with the nomenclature for inverse trigonometric functions. The latter are misnomers, since the prefix ''arc'' is the abbreviation for ''arcus'', while the prefix ''ar'' stands for ''area''.〔As stated by Jan Gullberg, ''Mathematics: From the Birth of Numbers'' (New York: W. W. Norton & Company, 1997), ISBN 0-393-04002-X, p. 539: Another form of notation, , , etc., is a practice to be condemned as these functions have nothing whatever to do with arc, but with area, as is demonstrated by their full Latin names, 〕〔As stated by Eberhard Zeidler, Wolfgang Hackbusch and Hans Rudolf Schwarz, translated by Bruce Hunt, ''Oxford Users' Guide to Mathematics'' (Oxford: Oxford University Press, 2004), ISBN 0-19-850763-1, Section 0.2.13: "The inverse hyperbolic functions", p. 68: "The Latin names for the inverse hyperbolic functions are area sinus hyperbolicus, area cosinus hyperbolicus, area tangens hyperbolicus and area cotangens hyperbolicus (of ''x''). ..." This aforesaid reference uses the notations arsinh, arcosh, artanh, and arcoth for the respective inverse hyperbolic functions.〕 〔As stated by Ilja N. Bronshtein, Konstantin A. Semendyayev, Gerhard Musiol and Heiner Muehlig, ''Handbook of Mathematics'' (Berlin: Springer-Verlag, 5th ed., 2007), ISBN 3-540-72121-5, , Section 2.10: "Area Functions", p. 91: The ''area functions'' are the inverse functions of the hyperbolic functions, i.e., the ''inverse hyperbolic functions''. The functions , , and are strictly monotone, so they have unique inverses without any restriction; the function cosh ''x'' has two monotonic intervals so we can consider two inverse functions. The name ''area'' refers to the fact that the geometric definition of the functions is the area of certain hyperbolic sectors ...〕 Other authors prefer to use the notation argsinh, argcosh, argtanh, and so on, where the prefix arg is the abbreviation of the Latin ''argumentum''. In computer science this is often shortened to ''asinh''. The notation , , etc., is also used, despite the fact that care must be taken to avoid misinterpretations of the superscript −1 as a power as opposed to a shorthand for inverse (e.g., versus 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「inverse hyperbolic function」の詳細全文を読む スポンサード リンク
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