Exponential function

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Antiderivative

∫ exp ⁡ z d z = exp ⁡ z + C {\displaystyle \int \exp z\,dz=\exp z+C}

At zero

1

Derivative

d d z exp ⁡ z = exp ⁡ z {\displaystyle {\frac {\mathrm {d} }{\mathrm {d} \!\,z}}\exp z=\exp z}

Domain

C {\displaystyle \mathbb {C} }

Fixed point

−Wn(−1) for n ∈ Z {\displaystyle n\in \mathbb {Z} }

General definition

exp ⁡ z = e z {\displaystyle \exp z=e^{z}}