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

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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[+]