# y0 man page

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.

## See Also

## Colophon

This page is part of release 4.08 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/.

## Referenced By

y0f(3), y0l(3), y1(3), y1f(3), y1l(3), yn(3), ynf(3) and ynl(3) are aliases of y0(3).