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Y0(3)                      Linux Programmer's Manual                     Y0(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(): _SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE
       y0f(), y0l(), y1f(), y1l(), ynf(), ynl(): _SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE >= 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, respec-
       tively.

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, respec-
       tively.  (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  func-
       tions.

       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.

CONFORMING TO
       The functions returning double conform to SVr4, 4.3BSD, POSIX.1-2001.  The others  are  non-standard  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 3.22 of the Linux man-pages project.  A description of the project,  and  informa-
       tion about reporting bugs, can be found at http://www.kernel.org/doc/man-pages/.



                                  2008-08-10                             Y0(3)