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


1. Differential Equation[-]

The function {\rm Ssi} \left( x \right) satisfies the differential equation with initial values y \left( 0 \right) =-\frac{\pi }{2}, y' \left( 0 \right) =1, and y'' \left( 0 \right) =0.

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 0 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 \infty [+]

6. Hypergeometric Representation[+]

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

8. Laplace Transform[+]