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

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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[+]