1Y0(3)                      Linux Programmer's Manual                     Y0(3)
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3
4

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>
11
12       double y0(double x);
13       double y1(double x);
14       double yn(int n, double x);
15
16       float y0f(float x);
17       float y1f(float x);
18       float ynf(int n, float x);
19
20       long double y0l(long double x);
21       long double y1l(long double x);
22       long double ynl(int n, long double x);
23
24       Link with -lm.
25
26   Feature Test Macro Requirements for glibc (see feature_test_macros(7)):
27
28       y0(), y1(), yn():
29           _XOPEN_SOURCE
30               || /* Since glibc 2.19: */ _DEFAULT_SOURCE
31               || /* Glibc versions <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
32       y0f(), y0l(), y1f(), y1l(), ynf(), ynl():
33           _XOPEN_SOURCE  >= 600
34               || (_ISOC99_SOURCE && _XOPEN_SOURCE)
35               || /* Since glibc 2.19: */ _DEFAULT_SOURCE
36               || /* Glibc versions <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
37

DESCRIPTION

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

RETURN VALUE

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

ERRORS

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

ATTRIBUTES

92       For  an  explanation  of  the  terms  used   in   this   section,   see
93       attributes(7).
94
95       ┌───────────────────┬───────────────┬─────────┐
96Interface          Attribute     Value   
97       ├───────────────────┼───────────────┼─────────┤
98y0(), y0f(), y0l() │ Thread safety │ MT-Safe │
99       ├───────────────────┼───────────────┼─────────┤
100y1(), y1f(), y1l() │ Thread safety │ MT-Safe │
101       ├───────────────────┼───────────────┼─────────┤
102yn(), ynf(), ynl() │ Thread safety │ MT-Safe │
103       └───────────────────┴───────────────┴─────────┘

CONFORMING TO

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

BUGS

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

SEE ALSO

122       j0(3)
123

COLOPHON

125       This page is part of release 5.07 of the Linux  man-pages  project.   A
126       description  of  the project, information about reporting bugs, and the
127       latest    version    of    this    page,    can     be     found     at
128       https://www.kernel.org/doc/man-pages/.
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132                                  2020-06-09                             Y0(3)
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