# Manpages - y0.3

## Table of Contents

## 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*():

_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) 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) 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).

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

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 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

*j0*(3)

## COLOPHON

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