SIMPLE SOLUTIONS

# J0(3) - man page online | library functions

Bessel functions of the first kind.

Chapter
2015-04-19
```J0(3)                               Linux Programmer's Manual                               J0(3)

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

SYNOPSIS
#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():
_SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE
j0f(), j0l(), j1f(), j1l(), jnf(), jnl():
_SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE >= 600

DESCRIPTION
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 val‐
ues.

RETURN VALUE
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
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
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 │
└───────────────────┴───────────────┴─────────┘
CONFORMING TO
The functions returning double conform to SVr4, 4.3BSD, POSIX.1-2001, and POSIX.1-2008.
The others are nonstandard functions that also exist on the BSDs.

BUGS
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.