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

rendering

1. Differential Equation[-]

The function {\rm arccsch} \left( x \right) satisfies the differential equation

2. Plot[+]

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

4. Expansion at 0[+]

5. 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..

5.1. Expansion at -i[+]

5.2. Expansion at i[+]

5.3. Expansion at \infty [+]

6. Hypergeometric Representation[+]

7. Laplace Transform[+]