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<h4 class="subsection">D.1.1 Bessel function calling conventions</h4>

<p><a name="index-bessel-functions-709"></a>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>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.

     <ul>
<li><code>J</code>
regular cylindrical Bessel functions
<li><code>Y</code>
irregular cylindrical Bessel functions
<li><code>I</code>
regular modified cylindrical Bessel functions
<li><code>K</code>
irregular modified cylindrical Bessel functions
</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">math</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>Two further related families of functions follow the same calling
convention.

     <ul>
<li><code>Isc</code>
scaled regular modified cylindrical Bessel functions
<li><code>Ksc</code>
scaled irregular modified cylindrical Bessel functions
</ul>

<p class="noindent">The foregoing functions are related to those above by an exponential scale
factor as documented in the gsl reference manual.

   <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>.

     <ul>
<li><code>j</code>
regular spherical Bessel functions
<li><code>y</code>
irregular spherical Bessel functions
<li><code>isc</code>
regular modified spherical Bessel functions
<li><code>ksc</code>
irregular modified spherical Bessel functions
</ul>

   <p>The functions in the remaining group follow idiosyncratic calling
conventions.

     <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><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><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. 
</ul>

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