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-/* yn.c
- *
- * Bessel function of second kind of integer order
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, yn();
- * int n;
- *
- * y = yn( n, x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order n, where n is a
- * (possibly negative) integer.
- *
- * The function is evaluated by forward recurrence on
- * n, starting with values computed by the routines
- * y0() and y1().
- *
- * If n = 0 or 1 the routine for y0 or y1 is called
- * directly.
- *
- *
- *
- * ACCURACY:
- *
- *
- * Absolute error, except relative
- * when y > 1:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 2200 2.9e-16 5.3e-17
- * IEEE 0, 30 30000 3.4e-15 4.3e-16
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * yn singularity x = 0 MAXNUM
- * yn overflow MAXNUM
- *
- * Spot checked against tables for x, n between 0 and 100.
- *
- */
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 2000 by Stephen L. Moshier
-*/
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double y0 ( double );
-extern double y1 ( double );
-extern double log ( double );
-#else
-double y0(), y1(), log();
-#endif
-extern double MAXNUM, MAXLOG;
-
-double yn( n, x )
-int n;
-double x;
-{
-double an, anm1, anm2, r;
-int k, sign;
-
-if( n < 0 )
- {
- n = -n;
- if( (n & 1) == 0 ) /* -1**n */
- sign = 1;
- else
- sign = -1;
- }
-else
- sign = 1;
-
-
-if( n == 0 )
- return( sign * y0(x) );
-if( n == 1 )
- return( sign * y1(x) );
-
-/* test for overflow */
-if( x <= 0.0 )
- {
- mtherr( "yn", SING );
- return( -MAXNUM );
- }
-
-/* forward recurrence on n */
-
-anm2 = y0(x);
-anm1 = y1(x);
-k = 1;
-r = 2 * k;
-do
- {
- an = r * anm1 / x - anm2;
- anm2 = anm1;
- anm1 = an;
- r += 2.0;
- ++k;
- }
-while( k < n );
-
-
-return( sign * an );
-}