# j0(3) — Linux manual page

```j0(3)                   Library Functions Manual                   j0(3)
```

## NAME         top

```       j0, j0f, j0l, j1, j1f, j1l, jn, jnf, jnl - Bessel functions of
the first kind
```

## LIBRARY         top

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

## SYNOPSIS         top

```       #include <math.h>

double j0(double x);
double j1(double x);
double jn(int n, double x);

float j0f(float x);
float j1f(float x);
float jnf(int n, float x);

long double j0l(long double x);
long double j1l(long double x);
long double jnl(int n, long double x);

Feature Test Macro Requirements for glibc (see
feature_test_macros(7)):

j0(), j1(), jn():
_XOPEN_SOURCE
|| /* Since glibc 2.19: */ _DEFAULT_SOURCE
|| /* glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE

j0f(), j0l(), j1f(), j1l(), jnf(), jnl():
_XOPEN_SOURCE >= 600
|| (_ISOC99_SOURCE && _XOPEN_SOURCE)
|| /* Since glibc 2.19: */ _DEFAULT_SOURCE
|| /* glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
```

## DESCRIPTION         top

```       The j0() and j1() functions return Bessel functions of x of the
first kind of orders 0 and 1, respectively.  The jn() function
returns the Bessel function of x of the first kind of order n.

The j0f(), j1f(), and jnf(), functions are versions that take and
return float values.  The j0l(), j1l(), and jnl() functions are
versions that take and return long double values.
```

## RETURN VALUE         top

```       On success, these functions return the appropriate Bessel value
of the first kind for x.

If x is a NaN, a NaN is returned.

If x is too large in magnitude, or the result underflows, a range
error occurs, and the return value is 0.
```

## 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:

Range error: result underflow, or x is too large in magnitude
errno is set to ERANGE.

These functions do not raise exceptions for fetestexcept(3).
```

## ATTRIBUTES         top

```       For an explanation of the terms used in this section, see
attributes(7).
┌─────────────────────────────────────┬───────────────┬─────────┐
│ Interface                           │ Attribute     │ Value   │
├─────────────────────────────────────┼───────────────┼─────────┤
│ j0(), j0f(), j0l()                  │ Thread safety │ MT-Safe │
├─────────────────────────────────────┼───────────────┼─────────┤
│ j1(), j1f(), j1l()                  │ Thread safety │ MT-Safe │
├─────────────────────────────────────┼───────────────┼─────────┤
│ jn(), jnf(), jnl()                  │ Thread safety │ MT-Safe │
└─────────────────────────────────────┴───────────────┴─────────┘
```

## STANDARDS         top

```       j0()
j1()
jn()   POSIX.1-2008.

Others:
BSD.
```

## HISTORY         top

```       j0()
j1()
jn()   SVr4, 4.3BSD, POSIX.1-2001, POSIX.1-2008.

Others:
BSD.
```

## BUGS         top

```       There are errors of up to 2e-16 in the values returned by j0(),
j1(), and jn() for values of x between -8 and 8.
```

```       y0(3)
```

## COLOPHON         top

```       This page is part of the man-pages (Linux kernel and C library
user-space interface documentation) project.  Information about
the project can be found at
⟨https://www.kernel.org/doc/man-pages/⟩.  If you have a bug report
for this manual page, see
⟨https://git.kernel.org/pub/scm/docs/man-pages/man-pages.git/tree/CONTRIBUTING⟩.