The Special Function  \arcsin \left( x \right)

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1. Differential Equation[-]

The function  \arcsin \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 -1 [+]

7.2. Expansion at 1 [+]

7.3. Expansion at \infty [+]

8. Hypergeometric Representation[+]

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