The Special Function {\rm erfc} \left( n,x \right)


1. Differential Equation[-]

The function {\rm erfc} \left( n,x \right) satisfies the differential equation with initial values y \left( 0 \right) =\frac{1}{{2}^{n}\,\Gamma \left( 1/2\,n+1 \right) } and y' \left( 0 \right) =-\frac{{2}^{1-n}}{\Gamma \left( 1/2\,n+1/2 \right) }.

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

3. Expansion at 0[+]

4. 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..

4.1. Expansion at \infty [+]

5. Hypergeometric Representation[+]

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

7. Laplace Transform[+]

8. Parameters[-]

The iterated integral of the complementary error function {\rm erfc} \left( n,x \right) depends on the parameter n. The box below can be used to rename or instantiate this parameter.
p1 =