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- <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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