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);

       Link with -lm.

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

       j0(), j1(), jn():
           _XOPEN_SOURCE
               || /* Since glibc 2.19: */ _DEFAULT_SOURCE
               || /* Glibc versions <= 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 versions <= 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 │
       └────────────────────┴───────────────┴─────────┘

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.

SEE ALSO

       y0(3)

COLOPHON

       This  page  is  part  of  release  5.10  of  the  Linux man-pages project.  A description of the project,
       information  about  reporting  bugs,  and  the  latest  version  of  this   page,   can   be   found   at
       https://www.kernel.org/doc/man-pages/.

                                                   2020-12-21                                              J0(3)