# Category:Exponential Function

This category contains results about the exponential function.

Definitions specific to this category can be found in Definitions/Exponential Function.

The **exponential function** can be defined as the unique solution $y = f \paren z$ to the first order ODE:

- $\dfrac {\d y} {\d z} = y$

satisfying the initial condition $f \paren 0 = 1$.

That is, the defining property of $\exp$ is that it is its own derivative.

## Subcategories

This category has the following 18 subcategories, out of 18 total.

### D

### E

### L

## Pages in category "Exponential Function"

The following 67 pages are in this category, out of 67 total.

### C

### E

- Equivalence of Definitions of Complex Exponential Function
- Equivalence of Definitions of Exponential Function
- Equivalence of Definitions of Real Exponential Function
- Euler's Formula
- Euler's Formula/Real Domain
- Euler's Number to Rational Power permits Unique Continuous Extension
- Exponent Combination Laws/Quotient of Powers
- Exponential Dominates Polynomial
- Exponential Function is Continuous
- Exponential Function is Differentiable
- Exponential Function is Well-Defined/Real
- Exponential is Strictly Convex
- Exponential is Strictly Increasing
- Exponential of Complex Number plus 2 pi i
- Exponential of Natural Logarithm
- Exponential of One
- Exponential of Product
- Exponential of Rational Number is Irrational
- Exponential of Real Number is Strictly Positive
- Exponential of Sum
- Exponential of x not less than 1+x
- Exponential of Zero
- Exponential of Zero and One
- Exponential on Complex Plane is Group Homomorphism
- Exponential on Real Numbers is Group Isomorphism
- Exponential on Real Numbers is Injection
- Exponential Sequence is Eventually Increasing
- Exponential Sequence is Eventually Strictly Positive
- Exponential Sequence is Uniformly Convergent on Compact Sets
- Exponential Tends to Zero and Infinity

### L

### M

### P

- Period of Complex Exponential Function
- Periodicity of Complex Exponential Function
- Power Series Expansion for Exponential Function
- Power Series Expansion for Exponential of Cosine of x
- Power Series Expansion for Exponential of Sine of x
- Power Series Expansion for Exponential of Tangent of x
- Power Series Expansion for Exponential of x by Cosine of x
- Power Series Expansion for Exponential of x by Sine of x
- Power Series Expansion for General Exponential Function
- Power Series Expansion for Integer Power of Exponential Function minus 1
- Properties of Complex Exponential Function
- Properties of Exponential Function