The inverse hyperbolic sine function.
xis a real or complex number
arcsinh is the inverse of the hyperbolic sine function. It is defined by
arcsinh(z) = ln(z + √(1 + z^2))
for all complex
arcsinh(x) is real for all real
This function is also called
arsinh (area hyperbolic sine) in the literature. Some authors claim that the name
arcsinh is a misnomer, but this depends crucially on how you view the connections between the trigonometric and the hyperbolic functions and their (restriction) inverses. One can argue that the name
arcsinh makes perfect sense.