### 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**() 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.
| |

### CONFORMING TO

The functions returning
*double* conform to SVr4, 4.3BSD,
POSIX.1-2001.
The others are non-standard 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 3.23 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/.