The Special Function  {{\rm e}^{x}}


1. Differential Equation[-]

The function  {{\rm e}^{x}} satisfies the differential equation with initial value y \left( 0 \right) =1 .

2. Plot[+]

3. Numerical Evaluation[+]

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

5. Expansion at 0 [+]

6. 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 ..

6.1. Expansion at \infty [+]

7. Hypergeometric Representation[+]

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

9. Laplace Transform[+]