# Y0

NAME
SYNOPSIS
DESCRIPTION
RETURN VALUE
ERRORS
ATTRIBUTES
CONFORMING TO
BUGS
COLOPHON

## 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);

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() etc. and y0l() etc. functions are versions that take and return float and long double values, respectively.

## 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.

## ATTRIBUTES

For an explanation of the terms used in this section, see attributes(7).

## 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.