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<html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><title>Funções</title><meta name="generator" content="DocBook XSL Stylesheets Vsnapshot"><link rel="home" href="index.html" title="Manual do Genius"><link rel="up" href="ch11.html" title="Chapter 11. List of GEL functions"><link rel="prev" href="ch11s11.html" title="Cálculo"><link rel="next" href="ch11s13.html" title="Solução de equações"></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Funções</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="ch11s11.html">Prev</a> </td><th width="60%" align="center">Chapter 11. List of GEL functions</th><td width="20%" align="right"> <a accesskey="n" href="ch11s13.html">Next</a></td></tr></table><hr></div><div class="sect1"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="genius-gel-function-list-functions"></a>Funções</h2></div></div></div><div class="variablelist"><dl class="variablelist"><dt><span lang="en" class="term"><a name="gel-function-Argument"></a>Argument</span></dt><dd><pre lang="en" class="synopsis">Argument (z)</pre><p lang="en">Aliases: <code class="function">Arg</code> <code class="function">arg</code></p><p lang="en">argument (angle) of complex number.</p></dd><dt><span lang="en" class="term"><a name="gel-function-BesselJ0"></a>BesselJ0</span></dt><dd><pre lang="en" class="synopsis">BesselJ0 (x)</pre><p lang="en">Bessel function of the first kind of order 0. Only implemented for real numbers.</p><p lang="en">
See
<a class="ulink" href="https://en.wikipedia.org/wiki/Bessel_functions" target="_top">Wikipedia</a> for more information.
</p><p lang="en">Version 1.0.16 onwards.</p></dd><dt><span lang="en" class="term"><a name="gel-function-BesselJ1"></a>BesselJ1</span></dt><dd><pre lang="en" class="synopsis">BesselJ1 (x)</pre><p lang="en">Bessel function of the first kind of order 1. Only implemented for real numbers.</p><p lang="en">
See
<a class="ulink" href="https://en.wikipedia.org/wiki/Bessel_functions" target="_top">Wikipedia</a> for more information.
</p><p lang="en">Version 1.0.16 onwards.</p></dd><dt><span lang="en" class="term"><a name="gel-function-BesselJn"></a>BesselJn</span></dt><dd><pre lang="en" class="synopsis">BesselJn (n,x)</pre><p lang="en">Bessel function of the first kind of order <code class="varname">n</code>. Only implemented for real numbers.</p><p lang="en">
See
<a class="ulink" href="https://en.wikipedia.org/wiki/Bessel_functions" target="_top">Wikipedia</a> for more information.
</p><p lang="en">Version 1.0.16 onwards.</p></dd><dt><span lang="en" class="term"><a name="gel-function-BesselY0"></a>BesselY0</span></dt><dd><pre lang="en" class="synopsis">BesselY0 (x)</pre><p lang="en">Bessel function of the second kind of order 0. Only implemented for real numbers.</p><p lang="en">
See
<a class="ulink" href="https://en.wikipedia.org/wiki/Bessel_functions" target="_top">Wikipedia</a> for more information.
</p><p lang="en">Version 1.0.16 onwards.</p></dd><dt><span lang="en" class="term"><a name="gel-function-BesselY1"></a>BesselY1</span></dt><dd><pre lang="en" class="synopsis">BesselY1 (x)</pre><p lang="en">Bessel function of the second kind of order 1. Only implemented for real numbers.</p><p lang="en">
See
<a class="ulink" href="https://en.wikipedia.org/wiki/Bessel_functions" target="_top">Wikipedia</a> for more information.
</p><p lang="en">Version 1.0.16 onwards.</p></dd><dt><span lang="en" class="term"><a name="gel-function-BesselYn"></a>BesselYn</span></dt><dd><pre lang="en" class="synopsis">BesselYn (n,x)</pre><p lang="en">Bessel function of the second kind of order <code class="varname">n</code>. Only implemented for real numbers.</p><p lang="en">
See
<a class="ulink" href="https://en.wikipedia.org/wiki/Bessel_functions" target="_top">Wikipedia</a> for more information.
</p><p lang="en">Version 1.0.16 onwards.</p></dd><dt><span lang="en" class="term"><a name="gel-function-DirichletKernel"></a>DirichletKernel</span></dt><dd><pre lang="en" class="synopsis">DirichletKernel (n,t)</pre><p lang="en">Dirichlet kernel of order <code class="varname">n</code>.</p></dd><dt><span lang="en" class="term"><a name="gel-function-DiscreteDelta"></a>DiscreteDelta</span></dt><dd><pre lang="en" class="synopsis">DiscreteDelta (v)</pre><p lang="en">Returns 1 if and only if all elements are zero.</p></dd><dt><span lang="en" class="term"><a name="gel-function-ErrorFunction"></a>ErrorFunction</span></dt><dd><pre lang="en" class="synopsis">ErrorFunction (x)</pre><p lang="en">Aliases: <code class="function">erf</code></p><p lang="en">The error function, 2/sqrt(pi) * int_0^x e^(-t^2) dt.</p><p lang="en">
See
<a class="ulink" href="https://en.wikipedia.org/wiki/Error_function" target="_top">Wikipedia</a> or
<a class="ulink" href="http://planetmath.org/ErrorFunction" target="_top">Planetmath</a> for more information.
</p></dd><dt><span lang="en" class="term"><a name="gel-function-FejerKernel"></a>FejerKernel</span></dt><dd><pre lang="en" class="synopsis">FejerKernel (n,t)</pre><p lang="en">Fejer kernel of order <code class="varname">n</code> evaluated at
<code class="varname">t</code></p><p lang="en">
See
<a class="ulink" href="http://planetmath.org/FejerKernel" target="_top">Planetmath</a> for more information.
</p></dd><dt><span lang="en" class="term"><a name="gel-function-GammaFunction"></a>GammaFunction</span></dt><dd><pre lang="en" class="synopsis">GammaFunction (x)</pre><p lang="en">Aliases: <code class="function">Gamma</code></p><p lang="en">The Gamma function. Currently only implemented for real values.</p><p lang="en">
See
<a class="ulink" href="http://planetmath.org/GammaFunction" target="_top">Planetmath</a> or
<a class="ulink" href="https://en.wikipedia.org/wiki/Gamma_function" target="_top">Wikipedia</a> for more information.
</p></dd><dt><span lang="en" class="term"><a name="gel-function-KroneckerDelta"></a>KroneckerDelta</span></dt><dd><pre lang="en" class="synopsis">KroneckerDelta (v)</pre><p lang="en">Returns 1 if and only if all elements are equal.</p></dd><dt><span lang="en" class="term"><a name="gel-function-LambertW"></a>LambertW</span></dt><dd><pre lang="en" class="synopsis">LambertW (x)</pre><p lang="en">
The principal branch of Lambert W function computed for only
real values greater than or equal to <strong class="userinput"><code>-1/e</code></strong>.
That is, <code class="function">LambertW</code> is the inverse of
the expression <strong class="userinput"><code>x*e^x</code></strong>. Even for
real <code class="varname">x</code> this expression is not one to one and
therefore has two branches over <strong class="userinput"><code>[-1/e,0)</code></strong>.
See <a class="link" href="ch11s12.html#gel-function-LambertWm1"><code class="function">LambertWm1</code></a> for the other real branch.
</p><p lang="en">
See
<a class="ulink" href="https://en.wikipedia.org/wiki/Lambert_W_function" target="_top">Wikipedia</a> for more information.
</p><p lang="en">Version 1.0.18 onwards.</p></dd><dt><span lang="en" class="term"><a name="gel-function-LambertWm1"></a>LambertWm1</span></dt><dd><pre lang="en" class="synopsis">LambertWm1 (x)</pre><p lang="en">
The minus-one branch of Lambert W function computed for only
real values greater than or equal to <strong class="userinput"><code>-1/e</code></strong>
and less than 0.
That is, <code class="function">LambertWm1</code> is the second
branch of the inverse of <strong class="userinput"><code>x*e^x</code></strong>.
See <a class="link" href="ch11s12.html#gel-function-LambertW"><code class="function">LambertW</code></a> for the principal branch.
</p><p lang="en">
See
<a class="ulink" href="https://en.wikipedia.org/wiki/Lambert_W_function" target="_top">Wikipedia</a> for more information.
</p></dd><dt><span lang="en" class="term"><a name="gel-function-MinimizeFunction"></a>MinimizeFunction</span></dt><dd><pre lang="en" class="synopsis">MinimizeFunction (func,x,incr)</pre><p lang="en">Find the first value where f(x)=0.</p></dd><dt><span lang="en" class="term"><a name="gel-function-MoebiusDiskMapping"></a>MoebiusDiskMapping</span></dt><dd><pre lang="en" class="synopsis">MoebiusDiskMapping (a,z)</pre><p lang="en">Moebius mapping of the disk to itself mapping a to 0.</p><p lang="en">
See
<a class="ulink" href="https://en.wikipedia.org/wiki/M%C3%B6bius_transformation" target="_top">Wikipedia</a> or
<a class="ulink" href="http://planetmath.org/MobiusTransformation" target="_top">Planetmath</a> for more information.
</p></dd><dt><span lang="en" class="term"><a name="gel-function-MoebiusMapping"></a>MoebiusMapping</span></dt><dd><pre lang="en" class="synopsis">MoebiusMapping (z,z2,z3,z4)</pre><p lang="en">Moebius mapping using the cross ratio taking z2,z3,z4 to 1,0, and infinity respectively.</p><p lang="en">
See
<a class="ulink" href="https://en.wikipedia.org/wiki/M%C3%B6bius_transformation" target="_top">Wikipedia</a> or
<a class="ulink" href="http://planetmath.org/MobiusTransformation" target="_top">Planetmath</a> for more information.
</p></dd><dt><span lang="en" class="term"><a name="gel-function-MoebiusMappingInftyToInfty"></a>MoebiusMappingInftyToInfty</span></dt><dd><pre lang="en" class="synopsis">MoebiusMappingInftyToInfty (z,z2,z3)</pre><p lang="en">Moebius mapping using the cross ratio taking infinity to infinity and z2,z3 to 1 and 0 respectively.</p><p lang="en">
See
<a class="ulink" href="https://en.wikipedia.org/wiki/M%C3%B6bius_transformation" target="_top">Wikipedia</a> or
<a class="ulink" href="http://planetmath.org/MobiusTransformation" target="_top">Planetmath</a> for more information.
</p></dd><dt><span lang="en" class="term"><a name="gel-function-MoebiusMappingInftyToOne"></a>MoebiusMappingInftyToOne</span></dt><dd><pre lang="en" class="synopsis">MoebiusMappingInftyToOne (z,z3,z4)</pre><p lang="en">Moebius mapping using the cross ratio taking infinity to 1 and z3,z4 to 0 and infinity respectively.</p><p lang="en">
See
<a class="ulink" href="https://en.wikipedia.org/wiki/M%C3%B6bius_transformation" target="_top">Wikipedia</a> or
<a class="ulink" href="http://planetmath.org/MobiusTransformation" target="_top">Planetmath</a> for more information.
</p></dd><dt><span lang="en" class="term"><a name="gel-function-MoebiusMappingInftyToZero"></a>MoebiusMappingInftyToZero</span></dt><dd><pre lang="en" class="synopsis">MoebiusMappingInftyToZero (z,z2,z4)</pre><p lang="en">Moebius mapping using the cross ratio taking infinity to 0 and z2,z4 to 1 and infinity respectively.</p><p lang="en">
See
<a class="ulink" href="https://en.wikipedia.org/wiki/M%C3%B6bius_transformation" target="_top">Wikipedia</a> or
<a class="ulink" href="http://planetmath.org/MobiusTransformation" target="_top">Planetmath</a> for more information.
</p></dd><dt><span lang="en" class="term"><a name="gel-function-PoissonKernel"></a>PoissonKernel</span></dt><dd><pre lang="en" class="synopsis">PoissonKernel (r,sigma)</pre><p lang="en">Poisson kernel on D(0,1) (not normalized to 1, that is integral of this is 2pi).</p></dd><dt><span lang="en" class="term"><a name="gel-function-PoissonKernelRadius"></a>PoissonKernelRadius</span></dt><dd><pre lang="en" class="synopsis">PoissonKernelRadius (r,sigma)</pre><p lang="en">Poisson kernel on D(0,R) (not normalized to 1).</p></dd><dt><span lang="en" class="term"><a name="gel-function-RiemannZeta"></a>RiemannZeta</span></dt><dd><pre lang="en" class="synopsis">RiemannZeta (x)</pre><p lang="en">Aliases: <code class="function">zeta</code></p><p lang="en">The Riemann zeta function. Currently only implemented for real values.</p><p lang="en">
See
<a class="ulink" href="http://planetmath.org/RiemannZetaFunction" target="_top">Planetmath</a> or
<a class="ulink" href="https://en.wikipedia.org/wiki/Riemann_zeta_function" target="_top">Wikipedia</a> for more information.
</p></dd><dt><span lang="en" class="term"><a name="gel-function-UnitStep"></a>UnitStep</span></dt><dd><pre lang="en" class="synopsis">UnitStep (x)</pre><p lang="en">The unit step function is 0 for x<0, 1 otherwise. This is the integral of the Dirac Delta function. Also called the Heaviside function.</p><p lang="en">
See
<a class="ulink" href="https://en.wikipedia.org/wiki/Unit_step" target="_top">Wikipedia</a> for more information.
</p></dd><dt><span lang="en" class="term"><a name="gel-function-cis"></a>cis</span></dt><dd><pre lang="en" class="synopsis">cis (x)</pre><p lang="en">
The <code class="function">cis</code> function, that is the same as
<strong class="userinput"><code>cos(x)+1i*sin(x)</code></strong>
</p></dd><dt><span lang="en" class="term"><a name="gel-function-deg2rad"></a>deg2rad</span></dt><dd><pre lang="en" class="synopsis">deg2rad (x)</pre><p lang="en">Convert degrees to radians.</p></dd><dt><span lang="en" class="term"><a name="gel-function-rad2deg"></a>rad2deg</span></dt><dd><pre lang="en" class="synopsis">rad2deg (x)</pre><p lang="en">Convert radians to degrees.</p></dd><dt><span lang="en" class="term"><a name="gel-function-sinc"></a>sinc</span></dt><dd><pre lang="en" class="synopsis">sinc (x)</pre><p lang="en">Calculates the unnormalized sinc function, that is
<strong class="userinput"><code>sin(x)/x</code></strong>.
If you want the normalized function call <strong class="userinput"><code>sinc(pi*x)</code></strong>.</p><p lang="en">
See
<a class="ulink" href="https://en.wikipedia.org/wiki/Sinc" target="_top">Wikipedia</a> for more information.
</p><p lang="en">Version 1.0.16 onwards.</p></dd></dl></div></div><div class="navfooter"><hr><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="ch11s11.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="ch11.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="ch11s13.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Cálculo </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> Solução de equações</td></tr></table></div></body></html>
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