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 

       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 featuretestmacros(7)):

       y0(), y1(), yn():
           SVIDSOURCE || BSDSOURCE || XOPENSOURCE
       y0f(), y0l(), y1f(), y1l(), ynf(), ynl():
           SVIDSOURCE || BSDSOURCE || XOPENSOURCE >= 600

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() etc. and y0l() etc. functions  are  versions  that  take  and
       return float and long double values, respectively.

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
       -HUGEVAL, -HUGEVALF, or -HUGEVALL, 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  -HUGEVAL,
       -HUGEVALF, or -HUGEVALL, 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
       -HUGEVAL, -HUGEVALF, or -HUGEVALL, respectively.  (POSIX.1-2001 also
       allows a 0.0 return for this case.)

ERRORS
       See matherror(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
              (FEINVALID) is raised.

       Pole error: x is 0.0
              errno is set to ERANGE (but see BUGS).  No  FEDIVBYZERO  excep‐
              tion is returned by fetestexcept(3) for this case.

       Range error: result underflow
              errno  is  set to ERANGE.  No FEUNDERFLOW 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 (FEOVERFLOW) 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.
       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  (FEINVALID)  when  a  domain error
       occurs.

SEE ALSO
       j0(3)

COLOPHON
       This page is part of release 3.53 of the Linux  man-pages  project.   A
       description  of  the project, and information about reporting bugs, can
       be found at http://www.kernel.org/doc/man-pages/.



                                  2008-08-10                             Y0(3)