PROLOG

       This  manual  page  is part of the POSIX Programmer's Manual.  The Linux implementation of this interface
       may differ (consult the corresponding Linux manual page for details of Linux behavior), or the  interface
       may not be implemented on Linux.

NAME

       y0, y1, yn — Bessel functions of the second kind

SYNOPSIS

       #include <math.h>

       double y0(double x);
       double y1(double x);
       double yn(int n, double x);

DESCRIPTION

       The y0(), y1(), and yn() functions shall compute Bessel functions of x of the second kind of orders 0, 1,
       and n, respectively.

       An   application   wishing   to   check   for  error  situations  should  set  errno  to  zero  and  call
       feclearexcept(FE_ALL_EXCEPT) before  calling  these  functions.  On  return,  if  errno  is  non-zero  or
       fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.

RETURN VALUE

       Upon  successful  completion,  these  functions shall return the relevant Bessel value of x of the second
       kind.

       If x is NaN, NaN shall be returned.

       If the x argument to these functions is negative, -HUGE_VAL or NaN shall be returned, and a domain  error
       may occur.

       If x is 0.0, -HUGE_VAL shall be returned and a pole error may occur.

       If the correct result would cause underflow, 0.0 shall be returned and a range error may occur.

       If  the  correct  result  would  cause overflow, -HUGE_VAL or 0.0 shall be returned and a range error may
       occur.

ERRORS

       These functions may fail if:

       Domain Error
                   The value of x is negative.

                   If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then  errno  shall  be
                   set  to  [EDOM].   If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero,
                   then the invalid floating-point exception shall be raised.

       Pole Error  The value of x is zero.

                   If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then  errno  shall  be
                   set  to [ERANGE].  If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero,
                   then the divide-by-zero floating-point exception shall be raised.

       Range Error The correct result would cause overflow.

                   If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then  errno  shall  be
                   set  to [ERANGE].  If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero,
                   then the overflow floating-point exception shall be raised.

       Range Error The value of x is too large in magnitude, or the correct result would cause underflow.

                   If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then  errno  shall  be
                   set  to [ERANGE].  If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero,
                   then the underflow floating-point exception shall be raised.

       The following sections are informative.

EXAMPLES

       None.

APPLICATION USAGE

       On error, the expressions (math_errhandling & MATH_ERRNO) and  (math_errhandling  &  MATH_ERREXCEPT)  are
       independent of each other, but at least one of them must be non-zero.

RATIONALE

       None.

FUTURE DIRECTIONS

       None.

SEE ALSO

       feclearexcept(), fetestexcept(), isnan(), j0()

       The Base Definitions volume of POSIX.1‐2017, Section 4.20, Treatment of Error Conditions for Mathematical
       Functions, <math.h>

COPYRIGHT

       Portions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1-2017, Standard
       for  Information  Technology  --  Portable  Operating  System  Interface  (POSIX),  The  Open  Group Base
       Specifications Issue 7, 2018 Edition, Copyright (C) 2018 by the Institute of Electrical  and  Electronics
       Engineers, Inc and The Open Group.  In the event of any discrepancy between this version and the original
       IEEE  and The Open Group Standard, the original IEEE and The Open Group Standard is the referee document.
       The original Standard can be obtained online at http://www.opengroup.org/unix/online.html .

       Any typographical or formatting errors that appear in this page are most likely to have  been  introduced
       during   the   conversion  of  the  source  files  to  man  page  format.  To  report  such  errors,  see
       https://www.kernel.org/doc/man-pages/reporting_bugs.html .

IEEE/The Open Group                                   2017                                            Y0(3POSIX)