---
name: "y0"
section: "3"
platform: "linux"
package: "man-pages"
version: "6.19-1"
release: "Arch Linux 2026-11-01"
platforms: ["linux", "freebsd"]
url: "https://new.carta.tech/y0"
---

# y0(3)

Bessel functions of the second kind

## NAME

y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl - Bessel functions of the second kind

## LIBRARY

Math library (*libm*, *-lm*)

## 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)](/feature_test_macros/7.md)):

**y0**(), **y1**(), **yn**():

```
    _XOPEN_SOURCE
        || /* Since glibc 2.19: */ _DEFAULT_SOURCE
        || /* glibc <= 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 <= 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)](/math_error/7.md) 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** and an **FE\_DIVBYZERO** exception is raised (but see BUGS).

- Range error: result underflow

  *errno* is set to **ERANGE**. No **FE\_UNDERFLOW** exception is returned by [**fetestexcept**(3)](/fetestexcept/3.md) for this case.

- Range error: result overflow

  *errno* is set to **ERANGE** (but see BUGS). An overflow floating-point exception (**FE\_OVERFLOW**) is raised.

## ATTRIBUTES

For an explanation of the terms used in this section, see [**attributes**(7)](/attributes/7.md).

| | | |
| --- | --- | --- |
| **Interface** | **Attribute** | **Value** |
| **y0**(), **y0f**(), **y0l**() | Thread safety | MT-Safe |
| **y1**(), **y1f**(), **y1l**() | Thread safety | MT-Safe |
| **yn**(), **ynf**(), **ynl**() | Thread safety | MT-Safe |

## STANDARDS

- **y0**() **y1**() **yn**()

  POSIX.1-2008.

- Others:

  BSD.

## HISTORY

- **y0**() **y1**() **yn**()

  SVr4, 4.3BSD, POSIX.1-2001.

- Others:

  BSD.

## BUGS

Before glibc 2.19, these functions misdiagnosed pole errors: *errno* was set to **EDOM**, instead of **ERANGE** and no **FE\_DIVBYZERO** exception was raised.

Before glibc 2.17, did not set *errno* for "range error: result underflow".

In glibc 2.3.2 and earlier, these functions do not raise an invalid floating-point exception (**FE\_INVALID**) when a domain error occurs.

## SEE ALSO

[**j0**(3)](/j0/3.md)