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

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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] [+]