jn(3) - f39

1j0(3)                      Library Functions Manual                      j0(3)
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NAME

6       j0,  j0f,  j0l,  j1,  j1f,  j1l, jn, jnf, jnl - Bessel functions of the
7       first kind
8

LIBRARY

10       Math library (libm, -lm)
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SYNOPSIS

13       #include <math.h>
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15       double j0(double x);
16       double j1(double x);
17       double jn(int n, double x);
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19       float j0f(float x);
20       float j1f(float x);
21       float jnf(int n, float x);
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23       long double j0l(long double x);
24       long double j1l(long double x);
25       long double jnl(int n, long double x);
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27   Feature Test Macro Requirements for glibc (see feature_test_macros(7)):
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29       j0(), j1(), jn():
30           _XOPEN_SOURCE
31               || /* Since glibc 2.19: */ _DEFAULT_SOURCE
32               || /* glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
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34       j0f(), j0l(), j1f(), j1l(), jnf(), jnl():
35           _XOPEN_SOURCE >= 600
36               || (_ISOC99_SOURCE && _XOPEN_SOURCE)
37               || /* Since glibc 2.19: */ _DEFAULT_SOURCE
38               || /* glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
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DESCRIPTION

41       The j0() and j1() functions return Bessel functions of x of  the  first
42       kind  of  orders  0 and 1, respectively.  The jn() function returns the
43       Bessel function of x of the first kind of order n.
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45       The j0f(), j1f(), and jnf(), functions are versions that take  and  re‐
46       turn  float values.  The j0l(), j1l(), and jnl() functions are versions
47       that take and return long double values.
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RETURN VALUE

50       On success, these functions return the appropriate Bessel value of  the
51       first kind for x.
52
53       If x is a NaN, a NaN is returned.
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55       If x is too large in magnitude, or the result underflows, a range error
56       occurs, and the return value is 0.
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ERRORS

59       See math_error(7) for information on how to determine whether an  error
60       has occurred when calling these functions.
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62       The following errors can occur:
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64       Range error: result underflow, or x is too large in magnitude
65              errno is set to ERANGE.
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67       These functions do not raise exceptions for fetestexcept(3).
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ATTRIBUTES

70       For  an  explanation  of  the  terms  used  in  this  section,  see at‐
71       tributes(7).
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73       ┌────────────────────────────────────────────┬───────────────┬─────────┐
74       │Interface                                   │ Attribute     │ Value   │
75       ├────────────────────────────────────────────┼───────────────┼─────────┤
76       │j0(), j0f(), j0l()                          │ Thread safety │ MT-Safe │
77       ├────────────────────────────────────────────┼───────────────┼─────────┤
78       │j1(), j1f(), j1l()                          │ Thread safety │ MT-Safe │
79       ├────────────────────────────────────────────┼───────────────┼─────────┤
80       │jn(), jnf(), jnl()                          │ Thread safety │ MT-Safe │
81       └────────────────────────────────────────────┴───────────────┴─────────┘
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STANDARDS

84       j0()
85       j1()
86       jn()   POSIX.1-2008.
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88       Others:
89              BSD.
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HISTORY

92       j0()
93       j1()
94       jn()   SVr4, 4.3BSD, POSIX.1-2001, POSIX.1-2008.
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96       Others:
97              BSD.
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BUGS

100       There are errors of up to 2e-16 in the values returned by  j0(),  j1(),
101       and jn() for values of x between -8 and 8.
102