y0(3) — Linux manual page


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

       y0(), y1(), yn():
               || /* Since glibc 2.19: */ _DEFAULT_SOURCE
               || /* Glibc <= 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 <= 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 and an FE_DIVBYZERO exception is
              raised (but see BUGS).

       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 set to ERANGE (but see BUGS).  An overflow
              floating-point exception (FE_OVERFLOW) is raised.

ATTRIBUTES         top

       For an explanation of the terms used in this section, see

       │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

       Before glibc 2.19, these functions misdiagnosed pole errors:
       errno was set to EDOM, instead of ERANGE and no FE_DIVBYZERO
       exception was raised.

       Before glibc 2.17, did not set errno for "range error: result

       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


COLOPHON         top

       This page is part of release 5.13 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

                               2021-03-22                          Y0(3)

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