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:

- 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)

This page is part of release 4.15 of the Linux `man-pages`

project. A description of the project, information about reporting bugs, and the latest version of this page, can be found at https://www.kernel.org/doc/man-pages/.