The inverse hyperbolic functions, sometimes also called the area hyperbolic functions (Spanier and Oldham 1987, p. 263) are the
function that are the inverse functions of
the hyperbolic functions. They are denoted
Variants of these notations beginning with a capital letter are commonly used to
denote their principal values (e.g., Harris and
Stocker 1998, p. 263).
These functions are
multivalued, and hence require branch cuts in the complex
plane. Differing branch cut conventions are possible, but those adopted in this
work follow those used by the Wolfram
Language, summarized below.
The inverse hyperbolic functions as defined in this work have the following
ranges for domains on the real line ,
again following the convention of the Wolfram
They are defined in the
complex plane by
See also Hyperbolic Functions
Inverse Hyperbolic Cotangent
Inverse Hyperbolic Secant
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of Integrals, Series, and Products, 6th ed. Harris, J. W. and Stocker, H. "Area Hyperbolic Functions."
New York: Springer-Verlag, pp. 263-273,
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§2.7 in Orlando, FL: Academic Press,
pp. 124-128, 2000. Handbook
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D. (Ed.). Boca Raton, FL: CRC Press, 1995. CRC
Standard Mathematical Tables and Formulae. Referenced
on Wolfram|Alpha Inverse Hyperbolic Functions
Cite this as:
Weisstein, Eric W. "Inverse Hyperbolic Functions."
From --A Wolfram Web Resource. MathWorld https://mathworld.wolfram.com/InverseHyperbolicFunctions.html