NAME | SYNOPSIS | DESCRIPTION | RETURN VALUE | ERRORS | ATTRIBUTES | CONFORMING TO | BUGS | SEE ALSO | COLOPHON

Y0(3)                     Linux Programmer's Manual                    Y0(3)

NAME         top

       y0,  y0f,  y0l,  y1, y1f, y1l, yn, ynf, ynl - Bessel functions of the
       second kind

SYNOPSIS         top

       #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         top

       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         top

       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         top

       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         top

       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         top

       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         top

       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         top

       j0(3)

COLOPHON         top

       This page is part of release 4.08 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)