y1(3) - f35

1Y0(3)                      Linux Programmer's Manual                     Y0(3)
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NAME

6       y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl - Bessel functions of the sec‐
7       ond kind
8

SYNOPSIS

10       #include <math.h>
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12       double y0(double x);
13       double y1(double x);
14       double yn(int n, double x);
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16       float y0f(float x);
17       float y1f(float x);
18       float ynf(int n, float x);
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20       long double y0l(long double x);
21       long double y1l(long double x);
22       long double ynl(int n, long double x);
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24       Link with -lm.
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26   Feature Test Macro Requirements for glibc (see feature_test_macros(7)):
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28       y0(), y1(), yn():
29           _XOPEN_SOURCE
30               || /* Since glibc 2.19: */ _DEFAULT_SOURCE
31               || /* Glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
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33       y0f(), y0l(), y1f(), y1l(), ynf(), ynl():
34           _XOPEN_SOURCE >= 600
35               || (_ISOC99_SOURCE && _XOPEN_SOURCE)
36               || /* Since glibc 2.19: */ _DEFAULT_SOURCE
37               || /* Glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
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DESCRIPTION

40       The y0() and y1() functions return Bessel functions of x of the  second
41       kind  of  orders  0 and 1, respectively.  The yn() function returns the
42       Bessel function of x of the second kind of order n.
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44       The value of x must be positive.
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46       The y0f(), y1f(), and ynf() functions are versions that take and return
47       float  values.  The y0l(), y1l(), and ynl() functions are versions that
48       take and return long double values.
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RETURN VALUE

51       On success, these functions return the appropriate Bessel value of  the
52       second kind for x.
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54       If x is a NaN, a NaN is returned.
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56       If  x  is  negative,  a  domain  error occurs, and the functions return
57       -HUGE_VAL, -HUGE_VALF, or -HUGE_VALL, respectively.  (POSIX.1-2001 also
58       allows a NaN return for this case.)
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60       If  x  is 0.0, a pole error occurs, and the functions return -HUGE_VAL,
61       -HUGE_VALF, or -HUGE_VALL, respectively.
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63       If the result underflows, a range error occurs, and the  functions  re‐
64       turn 0.0
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66       If the result overflows, a range error occurs, and the functions return
67       -HUGE_VAL, -HUGE_VALF, or -HUGE_VALL, respectively.  (POSIX.1-2001 also
68       allows a 0.0 return for this case.)
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ERRORS

71       See  math_error(7) for information on how to determine whether an error
72       has occurred when calling these functions.
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74       The following errors can occur:
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76       Domain error: x is negative
77              errno is set  to  EDOM.   An  invalid  floating-point  exception
78              (FE_INVALID) is raised.
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80       Pole error: x is 0.0
81              errno  is  set to ERANGE and an FE_DIVBYZERO exception is raised
82              (but see BUGS).
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84       Range error: result underflow
85              errno is set to ERANGE.  No FE_UNDERFLOW exception  is  returned
86              by fetestexcept(3) for this case.
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88       Range error: result overflow
89              errno  is  set  to ERANGE (but see BUGS).  An overflow floating-
90              point exception (FE_OVERFLOW) is raised.
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ATTRIBUTES

93       For an  explanation  of  the  terms  used  in  this  section,  see  at‐
94       tributes(7).
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96       ┌────────────────────────────────────────────┬───────────────┬─────────┐
97       │Interface                                   │ Attribute     │ Value   │
98       ├────────────────────────────────────────────┼───────────────┼─────────┤
99       │y0(), y0f(), y0l()                          │ Thread safety │ MT-Safe │
100       ├────────────────────────────────────────────┼───────────────┼─────────┤
101       │y1(), y1f(), y1l()                          │ Thread safety │ MT-Safe │
102       ├────────────────────────────────────────────┼───────────────┼─────────┤
103       │yn(), ynf(), ynl()                          │ Thread safety │ MT-Safe │
104       └────────────────────────────────────────────┴───────────────┴─────────┘
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CONFORMING TO

107       The  functions  returning double conform to SVr4, 4.3BSD, POSIX.1-2001,
108       POSIX.1-2008.  The others are nonstandard functions that also exist  on
109       the BSDs.
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BUGS

112       Before  glibc 2.19, these functions misdiagnosed pole errors: errno was
113       set to EDOM, instead  of  ERANGE  and  no  FE_DIVBYZERO  exception  was
114       raised.
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116       Before  glibc  2.17,  did not set errno for "range error: result under‐
117       flow".
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119       In glibc version 2.3.2 and earlier, these functions do not raise an in‐
120       valid floating-point exception (FE_INVALID) when a domain error occurs.
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COLOPHON

126       This  page  is  part of release 5.12 of the Linux man-pages project.  A
127       description of the project, information about reporting bugs,  and  the
128       latest     version     of     this    page,    can    be    found    at
129       https://www.kernel.org/doc/man-pages/.
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133                                  2021-03-22                             Y0(3)