1Y0(3) Linux Programmer's Manual Y0(3)
2
6 y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl - Bessel functions of the sec‐
7 ond kind
8
10 #include <math.h>
11 double y0(double x);
13 double y1(double x);
14 double yn(int n, double x);
15 float y0f(float x);
17 float y1f(float x);
18 float ynf(int n, float x);
19 long double y0l(long double x);
21 long double y1l(long double x);
22 long double ynl(int n, long double x);
23 Link with -lm.
25 Feature Test Macro Requirements for glibc (see feature_test_macros(7)):
27 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
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 The value of x must be positive.
44 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
50 On success, these functions return the appropriate Bessel value of the
51 second kind for x.
52 If x is a NaN, a NaN is returned.
54 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 If x is 0.0, a pole error occurs, and the functions return -HUGE_VAL,
60 -HUGE_VALF, or -HUGE_VALL, respectively.
61 If the result underflows, a range error occurs, and the functions
63 return 0.0
64 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
70 See math_error(7) for information on how to determine whether an error
71 has occurred when calling these functions.
72 The following errors can occur:
74 Domain error: x is negative
76 errno is set to EDOM. An invalid floating-point exception
77 (FE_INVALID) is raised.
78 Pole error: x is 0.0
80 errno is set to ERANGE (but see BUGS). No FE_DIVBYZERO excep‐
81 tion is returned by fetestexcept(3) for this case.
82 Range error: result underflow
84 errno is set to ERANGE. No FE_UNDERFLOW exception is returned
85 by fetestexcept(3) for this case.
86 Range error: result overflow
88 errno is not set for this case. An overflow floating-point
89 exception (FE_OVERFLOW) is raised.
90
92 For an explanation of the terms used in this section, see
93 attributes(7).
94 ┌───────────────────┬───────────────┬─────────┐
96 │Interface │ Attribute │ Value │
97 ├───────────────────┼───────────────┼─────────┤
98 │y0(), y0f(), y0l() │ Thread safety │ MT-Safe │
99 ├───────────────────┼───────────────┼─────────┤
100 │y1(), y1f(), y1l() │ Thread safety │ MT-Safe │
101 ├───────────────────┼───────────────┼─────────┤
102 │yn(), ynf(), ynl() │ Thread safety │ MT-Safe │
103 └───────────────────┴───────────────┴─────────┘
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
110 On a pole error, these functions set errno to EDOM, instead of ERANGE
111 as POSIX.1-2004 requires.
112 In glibc version 2.3.2 and earlier, these functions do not raise an
114 invalid floating-point exception (FE_INVALID) when a domain error
115 occurs.
116
118 j0(3)
119
121 This page is part of release 4.16 of the Linux man-pages project. A
122 description of the project, information about reporting bugs, and the
123 latest version of this page, can be found at
124 https://www.kernel.org/doc/man-pages/.
125 2017-09-15 Y0(3)