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 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 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.

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 4.15 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)