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<a name="Bessel-function-calling-conventions-1"></a>
<h3 class="subsection">D.1.1 Bessel function calling conventions</h3>

<a name="index-bessel-functions"></a>
<p>The virtual code interface simplifies the gsl C language API by
excluding the facilities for error estimates, omitting certain array
valued functions, and subsuming sets of related functions
within common ones where possible.
</p>
<p>The functions with names in the following group take an argument of
the form <code>(n,x)</code>, where <code>n</code> identifies the member of the
function family, and <code>x</code> is the argument to the function.
</p>
<ul>
<li> <code>J</code>
regular cylindrical Bessel functions
</li><li> <code>Y</code>
irregular cylindrical Bessel functions
</li><li> <code>I</code>
regular modified cylindrical Bessel functions
</li><li> <code>K</code>
irregular modified cylindrical Bessel functions
</li></ul>

<p>For these functions, <code>n</code> can be either a natural number encoded
as in <a href="Representation-of-Numeric-and-Textual-Data.html#Representation-of-Numeric-and-Textual-Data">Representation of Numeric and Textual Data</a>, or a floating
point number encoded as in <a href="math.html#math"><code>math</code></a>. The latter case specifies
functions of a fractional order. The relevant gsl function is called
based on the value and type of the parameter.
</p>
<p>Two further related families of functions follow the same calling
convention.
</p>
<ul>
<li> <code>Isc</code>
scaled regular modified cylindrical Bessel functions
</li><li> <code>Ksc</code>
scaled irregular modified cylindrical Bessel functions
</li></ul>

<p>The foregoing functions are related to those above by an exponential scale
factor as documented in the gsl reference manual.
</p>
<p>Functions with names in the following group also take an argument of
the form <code>(n,x)</code>, but are not defined for fractional orders and
so require a natural number for <code>n</code>.
</p>
<ul>
<li> <code>j</code>
regular spherical Bessel functions
</li><li> <code>y</code>
irregular spherical Bessel functions
</li><li> <code>isc</code>
regular modified spherical Bessel functions
</li><li> <code>ksc</code>
irregular modified spherical Bessel functions
</li></ul>

<p>The functions in the remaining group follow idiosyncratic calling
conventions.
</p>
<ul>
<li> <code>zJ0</code>, <code>zJ1</code>
These take a natural number <code>n</code> and return the <code>n</code>th root of
the regular cylindrical Bessel functions of order 0 or 1,
respectively.
</li><li> <code>zJnu</code>
This takes a pair <code>(nu,n)</code> where <code>nu</code> is the (fractional)
order of a regular cylindrical Bessel function, <code>n</code> is a natural
number. It returns the <code>n</code>th zero of the function.
</li><li> <code>lnKnu</code>
This takes a pair of floating point numbers <code>(nu,x)</code> where
<code>nu</code> is the (fractional) order of an irregular modified
cylindrical Bessel and <code>x</code> is the argument to the function,
and it returns the natural log of the function.
</li></ul>

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