NAME

       y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl - Bessel functions of the second 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 exception 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)