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<a name="Functions-and-Variables-for-Fourier-series"></a>
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<p>
Next: <a href="maxima_138.html#Functions-and-Variables-for-Poisson-series" accesskey="n" rel="next">Functions and Variables for Poisson series</a>, Previous: <a href="maxima_136.html#Introduction-to-Fourier-series" accesskey="p" rel="previous">Introduction to Fourier series</a>, Up: <a href="maxima_132.html#Sums-Products-and-Series" accesskey="u" rel="up">Sums Products and Series</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_368.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
</div>
<a name="Functions-and-Variables-for-Fourier-series-1"></a>
<h3 class="section">28.5 Functions and Variables for Fourier series</h3>
<a name="equalp"></a><a name="Item_003a-Series_002fdeffn_002fequalp"></a><dl>
<dt><a name="index-equalp"></a>Function: <strong>equalp</strong> <em>(<var>x</var>, <var>y</var>)</em></dt>
<dd>
<p>Returns <code>true</code> if <code>equal (<var>x</var>, <var>y</var>)</code> otherwise <code>false</code>
(doesn’t give an error message like <code>equal (x, y)</code> would do in this case).
</p>
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</div></p></dd></dl>
<a name="remfun"></a><a name="Item_003a-Series_002fdeffn_002fremfun"></a><dl>
<dt><a name="index-remfun"></a>Function: <strong>remfun</strong> <em><br> <tt>remfun</tt> (<var>f</var>, <var>expr</var>) <br> <tt>remfun</tt> (<var>f</var>, <var>expr</var>, <var>x</var>)</em></dt>
<dd>
<p><code>remfun (<var>f</var>, <var>expr</var>)</code> replaces all occurrences of <code><var>f</var>
(<var>arg</var>)</code> by <var>arg</var> in <var>expr</var>.
</p>
<p><code>remfun (<var>f</var>, <var>expr</var>, <var>x</var>)</code> replaces all occurrences of
<code><var>f</var> (<var>arg</var>)</code> by <var>arg</var> in <var>expr</var> only if <var>arg</var> contains
the variable <var>x</var>.
</p>
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</div></p></dd></dl>
<a name="funp"></a><a name="Item_003a-Series_002fdeffn_002ffunp"></a><dl>
<dt><a name="index-funp"></a>Function: <strong>funp</strong> <em><br> <tt>funp</tt> (<var>f</var>, <var>expr</var>) <br> <tt>funp</tt> (<var>f</var>, <var>expr</var>, <var>x</var>)</em></dt>
<dd>
<p><code>funp (<var>f</var>, <var>expr</var>)</code>
returns <code>true</code> if <var>expr</var> contains the function <var>f</var>.
</p>
<p><code>funp (<var>f</var>, <var>expr</var>, <var>x</var>)</code>
returns <code>true</code> if <var>expr</var> contains the function <var>f</var> and the variable
<var>x</var> is somewhere in the argument of one of the instances of <var>f</var>.
</p>
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</div></p></dd></dl>
<a name="absint"></a><a name="Item_003a-Series_002fdeffn_002fabsint"></a><dl>
<dt><a name="index-absint"></a>Function: <strong>absint</strong> <em><br> <tt>absint</tt> (<var>f</var>, <var>x</var>, <var>halfplane</var>) <br> <tt>absint</tt> (<var>f</var>, <var>x</var>) <br> <tt>absint</tt> (<var>f</var>, <var>x</var>, <var>a</var>, <var>b</var>)</em></dt>
<dd>
<p><code>absint (<var>f</var>, <var>x</var>, <var>halfplane</var>)</code>
returns the indefinite integral of <var>f</var> with respect to
<var>x</var> in the given halfplane (<code>pos</code>, <code>neg</code>, or <code>both</code>).
<var>f</var> may contain expressions of the form
<code>abs (x)</code>, <code>abs (sin (x))</code>, <code>abs (a) * exp (-abs (b) * abs (x))</code>.
</p>
<p><code>absint (<var>f</var>, <var>x</var>)</code> is equivalent to
<code>absint (<var>f</var>, <var>x</var>, pos)</code>.
</p>
<p><code>absint (<var>f</var>, <var>x</var>, <var>a</var>, <var>b</var>)</code> returns the definite integral
of <var>f</var> with respect to <var>x</var> from <var>a</var> to <var>b</var>.
<var>f</var> may include absolute values.
</p>
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·<a href="maxima_369.html#Category_003a-Integral-calculus">Integral calculus</a>
</div></p></dd></dl>
<a name="fourier"></a><a name="Item_003a-Series_002fdeffn_002ffourier"></a><dl>
<dt><a name="index-fourier"></a>Function: <strong>fourier</strong> <em>(<var>f</var>, <var>x</var>, <var>p</var>)</em></dt>
<dd>
<p>Returns a list of the Fourier coefficients of <code><var>f</var>(<var>x</var>)</code> defined
on the interval <code>[-p, p]</code>.
</p>
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<a name="foursimp"></a><a name="Item_003a-Series_002fdeffn_002ffoursimp"></a><dl>
<dt><a name="index-foursimp"></a>Function: <strong>foursimp</strong> <em>(<var>l</var>)</em></dt>
<dd>
<p>Simplifies <code>sin (n %pi)</code> to 0 if <code>sinnpiflag</code> is <code>true</code> and
<code>cos (n %pi)</code> to <code>(-1)^n</code> if <code>cosnpiflag</code> is <code>true</code>.
</p>
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·<a href="maxima_369.html#Category_003a-Trigonometric-functions">Trigonometric functions</a>
·<a href="maxima_369.html#Category_003a-Simplification-functions">Simplification functions</a>
</div></p></dd></dl>
<a name="sinnpiflag"></a><a name="Item_003a-Series_002fdefvr_002fsinnpiflag"></a><dl>
<dt><a name="index-sinnpiflag"></a>Option variable: <strong>sinnpiflag</strong></dt>
<dd><p>Default value: <code>true</code>
</p>
<p>See <code>foursimp</code>.
</p>
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</div></p></dd></dl>
<a name="cosnpiflag"></a><a name="Item_003a-Series_002fdefvr_002fcosnpiflag"></a><dl>
<dt><a name="index-cosnpiflag"></a>Option variable: <strong>cosnpiflag</strong></dt>
<dd><p>Default value: <code>true</code>
</p>
<p>See <code>foursimp</code>.
</p>
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</div></p></dd></dl>
<a name="fourexpand"></a><a name="Item_003a-Series_002fdeffn_002ffourexpand"></a><dl>
<dt><a name="index-fourexpand"></a>Function: <strong>fourexpand</strong> <em>(<var>l</var>, <var>x</var>, <var>p</var>, <var>limit</var>)</em></dt>
<dd>
<p>Constructs and returns the Fourier series from the list of Fourier coefficients
<var>l</var> up through <var>limit</var> terms (<var>limit</var> may be <code>inf</code>). <var>x</var>
and <var>p</var> have same meaning as in <code>fourier</code>.
</p>
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</div></p></dd></dl>
<a name="fourcos"></a><a name="Item_003a-Series_002fdeffn_002ffourcos"></a><dl>
<dt><a name="index-fourcos"></a>Function: <strong>fourcos</strong> <em>(<var>f</var>, <var>x</var>, <var>p</var>)</em></dt>
<dd>
<p>Returns the Fourier cosine coefficients for <code><var>f</var>(<var>x</var>)</code> defined on
<code>[0, <var>p</var>]</code>.
</p>
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</div></p></dd></dl>
<a name="foursin"></a><a name="Item_003a-Series_002fdeffn_002ffoursin"></a><dl>
<dt><a name="index-foursin"></a>Function: <strong>foursin</strong> <em>(<var>f</var>, <var>x</var>, <var>p</var>)</em></dt>
<dd>
<p>Returns the Fourier sine coefficients for <code><var>f</var>(<var>x</var>)</code> defined on
<code>[0, <var>p</var>]</code>.
</p>
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</div></p></dd></dl>
<a name="totalfourier"></a><a name="Item_003a-Series_002fdeffn_002ftotalfourier"></a><dl>
<dt><a name="index-totalfourier"></a>Function: <strong>totalfourier</strong> <em>(<var>f</var>, <var>x</var>, <var>p</var>)</em></dt>
<dd>
<p>Returns <code>fourexpand (foursimp (fourier (<var>f</var>, <var>x</var>, <var>p</var>)),
<var>x</var>, <var>p</var>, 'inf)</code>.
</p>
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</div></p></dd></dl>
<a name="fourint"></a><a name="Item_003a-Series_002fdeffn_002ffourint"></a><dl>
<dt><a name="index-fourint"></a>Function: <strong>fourint</strong> <em>(<var>f</var>, <var>x</var>)</em></dt>
<dd>
<p>Constructs and returns a list of the Fourier integral coefficients of
<code><var>f</var>(<var>x</var>)</code> defined on <code>[minf, inf]</code>.
</p>
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</div></p></dd></dl>
<a name="fourintcos"></a><a name="Item_003a-Series_002fdeffn_002ffourintcos"></a><dl>
<dt><a name="index-fourintcos"></a>Function: <strong>fourintcos</strong> <em>(<var>f</var>, <var>x</var>)</em></dt>
<dd>
<p>Returns the Fourier cosine integral coefficients for <code><var>f</var>(<var>x</var>)</code>
on <code>[0, inf]</code>.
</p>
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</div></p></dd></dl>
<a name="forintsin"></a><a name="Item_003a-Series_002fdeffn_002ffourintsin"></a><dl>
<dt><a name="index-fourintsin"></a>Function: <strong>fourintsin</strong> <em>(<var>f</var>, <var>x</var>)</em></dt>
<dd>
<p>Returns the Fourier sine integral coefficients for <code><var>f</var>(<var>x</var>)</code> on
<code>[0, inf]</code>.
</p>
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</div></p></dd></dl>
<a name="Item_003a-Series_002fnode_002fFunctions-and-Variables-for-Poisson-series"></a><hr>
<div class="header">
<p>
Next: <a href="maxima_138.html#Functions-and-Variables-for-Poisson-series" accesskey="n" rel="next">Functions and Variables for Poisson series</a>, Previous: <a href="maxima_136.html#Introduction-to-Fourier-series" accesskey="p" rel="previous">Introduction to Fourier series</a>, Up: <a href="maxima_132.html#Sums-Products-and-Series" accesskey="u" rel="up">Sums Products and Series</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_368.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
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