y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl - Bessel functions of the second kind
#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
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.
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.)
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.
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 |
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.
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.
j0(3)