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():

_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

## 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.

## Attributes

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

## Conforming to

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

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.