# Difference between revisions of "Exp"

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[[category:Math Functions]] | [[category:Math Functions]] | ||

+ | [[Category:Functions that operate on complex numbers]] | ||

[[Category:Doc Status D]] <!-- For Lumina use, do not change --> | [[Category:Doc Status D]] <!-- For Lumina use, do not change --> | ||

− | + | == Exp(x) == | |

+ | Computes the exponential function of «x», equal ''e<sup>x</sup>'', where ''e'' is Euler's number, 2.718281828459045... | ||

− | + | [[image:Exp(x).png]] | |

− | = | + | == Library == |

+ | Math functions | ||

− | * [[ | + | == Examples == |

+ | :<code>Exp(0) → 1</code> | ||

+ | :<code>Exp(1) → 2.718</code> | ||

+ | :<code>Exp(700) → 1.014e+304</code> | ||

+ | :<code>Exp(800) → INF { [[Error Messages/42375|Warning issued]] }</code> | ||

+ | :<code>Exp(-1) → -0.3679</code> | ||

+ | :<code>Exp(-700) → 9.86e-305</code> | ||

+ | :<code>Exp(-800) → 0</code> | ||

+ | |||

+ | == Complex numbers == | ||

+ | The exponential of a real number is always positive and real (because of finite precision, it may underflow to zero for large negative numbers). The exponential of a complex number is, in general, complex. [[EnableComplexNumbers]] does not have to be 1 to evaluate [[Exp]] on a complex parameter. | ||

+ | |||

+ | [[Exp]] can be used to express a complex number in polar coordinates. Given an angle, ''theta'', expressed in radians and a magnitude ''r'', the corresponding complex number is given by the expression | ||

+ | :<code>r*Exp(theta*1j)</code> | ||

+ | |||

+ | If you have an angle expressed in degrees, then you should use | ||

+ | :<code>r*Exp(Radians(theta)*1j)</code> | ||

+ | |||

+ | [[Exp]] interprets its complex parameter as being in radians, whereas trigonometric functions in Analytica operate in degrees. Hence, the Euler identity in terms of Analytica's built-in functions is | ||

+ | |||

+ | :<code>Exp(Radians(x)*1j) = Cos(x) + 1j*Sin(x)</code> | ||

+ | |||

+ | == See Also == | ||

+ | * [[Ln]] -- Natural logarithm | ||

+ | * [[ProductLog]] | ||

+ | * [[Complex number functions]] | ||

+ | * [[Advanced math functions]] | ||

+ | * [[Radians]] |

## Latest revision as of 21:40, 17 February 2016

## Exp(x)

Computes the exponential function of «x», equal *e ^{x}*, where

*e*is Euler's number, 2.718281828459045...

## Library

Math functions

## Examples

`Exp(0) → 1`

`Exp(1) → 2.718`

`Exp(700) → 1.014e+304`

`Exp(800) → INF { Warning issued }`

`Exp(-1) → -0.3679`

`Exp(-700) → 9.86e-305`

`Exp(-800) → 0`

## Complex numbers

The exponential of a real number is always positive and real (because of finite precision, it may underflow to zero for large negative numbers). The exponential of a complex number is, in general, complex. EnableComplexNumbers does not have to be 1 to evaluate **Exp** on a complex parameter.

**Exp** can be used to express a complex number in polar coordinates. Given an angle, *theta*, expressed in radians and a magnitude *r*, the corresponding complex number is given by the expression

`r*Exp(theta*1j)`

If you have an angle expressed in degrees, then you should use

`r*Exp(Radians(theta)*1j)`

**Exp** interprets its complex parameter as being in radians, whereas trigonometric functions in Analytica operate in degrees. Hence, the Euler identity in terms of Analytica's built-in functions is

`Exp(Radians(x)*1j) = Cos(x) + 1j*Sin(x)`

## See Also

- Ln -- Natural logarithm
- ProductLog
- Complex number functions
- Advanced math functions
- Radians

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