# y0(3) — Linux manual page

```y0(3)                   Library Functions Manual                   y0(3)
```

## NAME         top

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

## LIBRARY         top

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

## SYNOPSIS         top

```       #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)):

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         top

```       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         top

```       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         top

```       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         top

```       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 │
└──────────────────────────────────────┴───────────────┴─────────┘
```

## STANDARDS         top

```       y0()
y1()
yn()   POSIX.1-2008.

Others:
BSD.
```

## HISTORY         top

```       y0()
y1()
yn()   SVr4, 4.3BSD, POSIX.1-2001.

Others:
BSD.
```

## BUGS         top

```       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.
```

```       j0(3)