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Y0(3)			   Linux Programmer's Manual			 Y0(3)

NAME
       y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl - Bessel functions of the sec‐
       ond kind

SYNOPSIS
       #include <math.h>

       double y0(double x);
       double y1(double x);
       double yn(int n, double x);

       float y0f(float x);
       float y1f(float x);
       float ynf(int n, float x);

       long double y0l(long double x);
       long double y1l(long double x);
       long double ynl(int n, long double x);

       Link with -lm.

   Feature Test Macro Requirements for glibc (see feature_test_macros(7)):

       y0(), y1(), yn():
	   _SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE
       y0f(), y0l(), y1f(), y1l(), ynf(), ynl():
	   _SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE >= 600

DESCRIPTION
       The y0() and y1() functions return Bessel functions of x of the	second
       kind  of	 orders	 0 and 1, respectively.	 The yn() function returns the
       Bessel function of x of the second kind of order n.

       The value of x must be positive.

       The y0f() etc. and y0l() etc. functions	are  versions  that  take  and
       return float and long double values, respectively.

RETURN VALUE
       On  success, these functions return the appropriate Bessel value of the
       second kind for x.

       If x is a NaN, a NaN is returned.

       If x is negative, a domain  error  occurs,  and	the  functions	return
       -HUGE_VAL, -HUGE_VALF, or -HUGE_VALL, respectively.  (POSIX.1-2001 also
       allows a NaN return for this case.)

       If x is 0.0, a pole error occurs, and the functions  return  -HUGE_VAL,
       -HUGE_VALF, or -HUGE_VALL, respectively.

       If  the	result	underflows,  a	range  error occurs, and the functions
       return 0.0

       If the result overflows, a range error occurs, and the functions return
       -HUGE_VAL, -HUGE_VALF, or -HUGE_VALL, respectively.  (POSIX.1-2001 also
       allows a 0.0 return for this case.)

ERRORS
       See math_error(7) for information on how to determine whether an	 error
       has occurred when calling these functions.

       The following errors can occur:

       Domain error: x is negative
	      errno  is	 set  to  EDOM.	  An  invalid floating-point exception
	      (FE_INVALID) is raised.

       Pole error: x is 0.0
	      errno is set to ERANGE (but see BUGS).  No  FE_DIVBYZERO	excep‐
	      tion is returned by fetestexcept(3) for this case.

       Range error: result underflow
	      errno  is	 set to ERANGE.	 No FE_UNDERFLOW exception is returned
	      by fetestexcept(3) for this case.

       Range error: result overflow
	      errno is not set for  this  case.	  An  overflow	floating-point
	      exception (FE_OVERFLOW) is raised.

CONFORMING TO
       The  functions  returning double conform to SVr4, 4.3BSD, POSIX.1-2001.
       The others are nonstandard functions that also exist on the BSDs.

BUGS
       On a pole error, these functions set errno to EDOM, instead  of	ERANGE
       as POSIX.1-2004 requires.

       In  glibc  version  2.3.2  and earlier, these functions do not raise an
       invalid floating-point  exception  (FE_INVALID)	when  a	 domain	 error
       occurs.

SEE ALSO
       j0(3)

COLOPHON
       This  page  is  part of release 3.54 of the Linux man-pages project.  A
       description of the project, and information about reporting  bugs,  can
       be found at http://www.kernel.org/doc/man-pages/.

				  2008-08-10				 Y0(3)
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