y0

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  re-
       turn 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 ex-
              ception (FE_OVERFLOW) is raised.

ATTRIBUTES
       For an  explanation  of  the  terms  used  in  this  section,  see  at-
       tributes(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 in-
       valid floating-point exception (FE_INVALID) when a domain error occurs.

SEE ALSO
       j0(3)

COLOPHON
       This  page  is  part of release 5.05 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/.

                                  2017-09-15                             Y0(3)