<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">x</font> be   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">q</font> being   <a href="rat_1.html#NM1" title="RAT_1:NM.1">Rational</a> holds  <span class="p1">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Olive" title="b1">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">q</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c1">x</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">q</font> be   <a href="rat_1.html#NM1" title="RAT_1:NM.1">Rational</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c1">x</font></span>)</span></span><br/>



<a NAME="E1:10"/>
 ex <font color="Olive" title="b1">m</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> ex <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>( <font color="Olive" title="b2">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">m</font> <a href="real_1.html#K6" title="REAL_1:func.6">/</a> <font color="Olive" title="b2">n</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rat_1.html#T8" title="RAT_1:th.8">RAT_1:8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:10"/>
<span class="p1">(<span class="default"><a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="prepower.html#K9" title="PREPOWER:func.9">#R</a> <font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sin_cos.html#K26" title="SIN_COS:func.26">exp_R</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">q</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c1">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="taylor_1.html#T6" target="_self" title="TAYLOR_1:th.6">Th6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
