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


1. Differential Equation[-]

The function {\rm arcsinh} \left( x \right) satisfies the differential equation with initial values y \left( 0 \right) =0 and y' \left( 0 \right) =1.

2. Plot[+]

3. Numerical Evaluation[+]

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

5. Symmetries[+]

6. Expansion at 0[+]

7. 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..

7.1. Expansion at -i[+]

7.2. Expansion at i[+]

7.3. Expansion at \infty [+]

8. Hypergeometric Representation[+]

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

10. Laplace Transform[+]