Difference between revisions of "Exp"
Line 1: Line 1:
 
[[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 -->
  
Line 5: Line 6:
  
 
Computes the exponential function of «x», equal ''e<sup>x</sup>'', where ''e'' is Euler's number, ''e=2.718281828459045...''
 
Computes the exponential function of «x», equal ''e<sup>x</sup>'', where ''e'' is Euler's number, ''e=2.718281828459045...''
 +
 +
[[image:Exp(x).png]]
  
 
= Library =
 
= Library =
  
 
Math functions
 
Math functions
 +
 +
= Examples =
 +
 +
:<code>Exp(0)</code> &rarr; 1
 +
:<code>Exp(1)</code> &rarr; 2.718
 +
:<code>Exp(700)</code> &rarr; 1.014e+304
 +
:<code>Exp(800)</code> &rarr; [[INF]]      ''&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{[[Error Messages/42375|Warning issued]]}''
 +
:<code>Exp(-1)</code> &rarr; -0.3679
 +
:<code>Exp(-700)</code> &rarr; 9.86e-305
 +
:<code>Exp(-800)</code> &rarr; 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 <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 =
 
= See Also =

Revision as of 19:55, 15 April 2013


Exp(x)

Computes the exponential function of «x», equal ex, where e is Euler's number, e=2.718281828459045...

Exp(x).png

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


You are not allowed to post comments.

Comments
<comments />