#### 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(), 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
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
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.
#### CONFORMING TO
The functions returning __double__ conform to SVr4, 4.3BSD, POSIX.1-2001.
The others are nonstandard 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 3.65 of the Linux __man-pages__ project. A
description of the project, and information about reporting bugs, can
be found at http://www.kernel.org/doc/man-pages/.
2014-01-18 Y0(3)
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