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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(), 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
              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 3.65 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/.

                                  2014-01-18                             Y0(3)



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