Difference between revisions of "Exp"

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)

@@ Line 3: / Line 3: @@
 [[Category:Doc Status D]] <!-- For Lumina use, do not change -->
-= Exp(x) =
+== Exp(x) ==
+Computes the exponential function of «x», equal ''e<sup>x</sup>'', where ''e'' is Euler's number, 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
-= Examples =
+== Examples ==
+:<code>Exp(0) &rarr; 1</code>
+:<code>Exp(1) &rarr; 2.718</code>
+:<code>Exp(700) &rarr; 1.014e+304</code>
+:<code>Exp(800) &rarr; INF     { [[Error Messages/42375|Warning issued]] }</code>
+:<code>Exp(-1) &rarr; -0.3679</code>
+:<code>Exp(-700) &rarr; 9.86e-305</code>
+:<code>Exp(-800) &rarr; 0</code>
-:<code>Exp(0)</code> &rarr; 1
+== Complex numbers ==
-:<code>Exp(1)</code> &rarr; 2.718
+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.
-:<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>
-[[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>.
+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>
+:<code>Exp(Radians(x)*1j) = Cos(x) + 1j*Sin(x)</code>
-= See Also =
-* [[Ln]]: Natural logarithm
-<comments />
+== See Also ==
+* [[Ln]] -- Natural logarithm
+* [[ProductLog]]
+* [[Complex number functions]]
+* [[Advanced math functions]]
+* [[Radians]]