The Special Function {\rm arccosh} \left( x \right)

rendering

1. Differential Equation[-]

The function {\rm arccosh} \left( x \right) satisfies the differential equation with initial values y \left( 0 \right) =\frac{i\pi }{2} and y' \left( 0 \right) =-i.

2. Plot[+]

3. Numerical Evaluation[+]

4. Derivative in Terms of Lower-Order Derivatives[+]

5. Expansion at 0[+]

6. Local Expansions at Singularities and at Infinity[-]

The differential equation above has 2 non-zero finite singular pointsA complex numberĀ z_0 is a singular point (or singularity of a linear ordinary differential equation with polynomial coefficients, if the leading coefficient of the equation vanishes atĀ z_0..

6.1. Expansion at -1[+]

6.2. Expansion at 1[+]

6.3. Expansion at \infty [+]

7. Hypergeometric Representation[+]

8. Chebyshev Expansion over [-1,1][+]