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():
	   _XOPEN_SOURCE
	       || /* Since glibc 2.19: */ _DEFAULT_SOURCE
	       || /* Glibc versions <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
       y0f(), y0l(), y1f(), y1l(), ynf(), ynl():
	   _XOPEN_SOURCE  >= 600
	       || (_ISOC99_SOURCE && _XOPEN_SOURCE)
	       || /* Since glibc 2.19: */ _DEFAULT_SOURCE
	       || /* Glibc versions <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE

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(), y1f(), and ynf() functions are versions that take and return
       float  values.  The y0l(), y1l(), and ynl() functions are versions that
       take and return long double values.

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.

ATTRIBUTES
       For  an	explanation  of	 the  terms  used   in	 this	section,   see
       attributes(7).

       +-------------------+---------------+---------+
       |Interface	   | Attribute	   | Value   |
       +-------------------+---------------+---------+
       |y0(), y0f(), y0l() | Thread safety | MT-Safe |
       +-------------------+---------------+---------+
       |y1(), y1f(), y1l() | Thread safety | MT-Safe |
       +-------------------+---------------+---------+
       |yn(), ynf(), ynl() | Thread safety | MT-Safe |
       +-------------------+---------------+---------+
CONFORMING TO
       The  functions  returning double conform to SVr4, 4.3BSD, POSIX.1-2001,
       POSIX.1-2008.  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 4.10 of the Linux  man-pages  project.   A
       description  of	the project, information about reporting bugs, and the
       latest	 version    of	  this	  page,	   can	   be	  found	    at
       https://www.kernel.org/doc/man-pages/.



				  2016-03-15				 Y0(3)