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)):
_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:
x
is negativeerrno
is set to EDOM. An invalid
floating-point exception (FE_INVALID) is raised.
x
is 0.0errno
is set to ERANGE and an
FE_DIVBYZERO exception is raised (but see BUGS).
errno
is set to ERANGE. No
FE_UNDERFLOW exception is returned by
fetestexcept(3) for this case.
errno
is set to ERANGE (but see BUGS). An
overflow floating-point exception (FE_OVERFLOW) is
raised.
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.
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 underflow".
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)
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