NAME

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

LIBRARY

       Math library (libm, -lm)

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():
           _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

       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

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

STANDARDS

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

       Others:
              BSD.

HISTORY

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

       Others:
              BSD.

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.

SEE ALSO

       y0(3)