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

Attributes

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

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.

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 longdouble values.

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).

History

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

       Others:
              BSD.

Library

       Math library (libm, -lm)

Name

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

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.

See Also

y0(3)

Linux man-pages 6.9.1                              2024-05-02                                              j0(3)

Standards

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

       Others:
              BSD.

Synopsis

#include<math.h>doublej0(doublex);doublej1(doublex);doublejn(intn,doublex);floatj0f(floatx);floatj1f(floatx);floatjnf(intn,floatx);longdoublej0l(longdoublex);longdoublej1l(longdoublex);longdoublejnl(intn,longdoublex);

   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

See Also