ynl(3)

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 4.09 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/.

                              2016-03-15                             Y0(3)

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