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():
           _XOPEN_SOURCE
               || /* Since glibc 2.19: */ _DEFAULT_SOURCE
               || /* Glibc <= 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 <= 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 and an FE_DIVBYZERO exception is raised (but see BUGS).

       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 set to ERANGE  (but  see  BUGS).   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

       Before glibc 2.19, these functions misdiagnosed  pole  errors:  errno  was  set  to  EDOM,
       instead of ERANGE and no FE_DIVBYZERO exception was raised.

       Before glibc 2.17, did not set errno for "range error: result underflow".

       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 5.13 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/.

                                            2021-03-22                                      Y0(3)