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<a name="jN_002c-jNf_002c-yN_002c-yNf_002d_002d_002dBessel-functions"></a>
<h3 class="section">1.10 <code>jN</code>, <code>jNf</code>, <code>yN</code>, <code>yNf</code>&mdash;Bessel functions</h3>
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<p><strong>Synopsis</strong>
</p><div class="example">
<pre class="example">#include &lt;math.h&gt;
double j0(double <var>x</var>);
float j0f(float <var>x</var>);
double j1(double <var>x</var>);
float j1f(float <var>x</var>);
double jn(int <var>n</var>, double <var>x</var>);
float jnf(int <var>n</var>, float <var>x</var>);
double y0(double <var>x</var>);
float y0f(float <var>x</var>);
double y1(double <var>x</var>);
float y1f(float <var>x</var>);
double yn(int <var>n</var>, double <var>x</var>);
float ynf(int <var>n</var>, float <var>x</var>);

</pre></div>
<p><strong>Description</strong><br>
The Bessel functions are a family of functions that solve the
differential equation 
</p><div class="smallexample">
<pre class="smallexample">  2               2    2
 x  y'' + xy' + (x  - p )y  = 0
</pre></div>
<p>These functions have many applications in engineering and physics.
</p>
<p><code>jn</code> calculates the Bessel function of the first kind of order
<var>n</var>.  <code>j0</code> and <code>j1</code> are special cases for order 0 and order
1 respectively.
</p>
<p>Similarly, <code>yn</code> calculates the Bessel function of the second kind of
order <var>n</var>, and <code>y0</code> and <code>y1</code> are special cases for order 0 and
1.
</p>
<p><code>jnf</code>, <code>j0f</code>, <code>j1f</code>, <code>ynf</code>, <code>y0f</code>, and <code>y1f</code> perform the
same calculations, but on <code>float</code> rather than <code>double</code> values.
</p>
<br>
<p><strong>Returns</strong><br>
The value of each Bessel function at <var>x</var> is returned.
</p>
<br>
<p><strong>Portability</strong><br>
None of the Bessel functions are in ANSI C.
</p>
<br>


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