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/* iv.c
*
* Modified Bessel function of noninteger order
*
*
*
* SYNOPSIS:
*
* double v, x, y, iv();
*
* y = iv( v, x );
*
*
*
* DESCRIPTION:
*
* Returns modified Bessel function of order v of the
* argument. If x is negative, v must be integer valued.
*
* The function is defined as Iv(x) = Jv( ix ). It is
* here computed in terms of the confluent hypergeometric
* function, according to the formula
*
* v -x
* Iv(x) = (x/2) e hyperg( v+0.5, 2v+1, 2x ) / Gamma(v+1)
*
* If v is a negative integer, then v is replaced by -v.
*
*
* ACCURACY:
*
* Tested at random points (v, x), with v between 0 and
* 30, x between 0 and 28.
* Relative error:
* arithmetic domain # trials peak rms
* DEC 0,30 2000 3.1e-15 5.4e-16
* IEEE 0,30 10000 1.7e-14 2.7e-15
*
* Accuracy is diminished if v is near a negative integer.
*
* See also hyperg.c.
*
*/
/* iv.c */
/* Modified Bessel function of noninteger order */
/* If x < 0, then v must be an integer. */
/*
Cephes Math Library Release 2.1: November, 1988
Copyright 1984, 1987, 1988 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
#include "mconf.h"
#ifndef ANSIPROT
double hyperg(), exp(), Gamma(), log(), fabs(), floor();
#endif
extern double MACHEP, MAXNUM, NAN;
double iv( v, x )
double v, x;
{
int sign;
double t, ax;
/* If v is a negative integer, invoke symmetry */
t = floor(v);
if( v < 0.0 )
{
if( t == v )
{
v = -v; /* symmetry */
t = -t;
}
}
/* If x is negative, require v to be an integer */
sign = 1;
if( x < 0.0 )
{
if( t != v )
{
mtherr( "iv", DOMAIN );
return( NAN );
}
if( v != 2.0 * floor(v/2.0) )
sign = -1;
}
/* Avoid logarithm singularity */
if( x == 0.0 )
{
if( v == 0.0 )
return( 1.0 );
if( v < 0.0 )
{
mtherr( "iv", OVERFLOW );
return( MAXNUM );
}
else
return( 0.0 );
}
ax = fabs(x);
t = v * log( 0.5 * ax ) - x;
t = sign * exp(t) / Gamma( v + 1.0 );
ax = v + 0.5;
return( t * hyperg( ax, 2.0 * ax, 2.0 * x ) );
}
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