1Y0(3) Linux Programmer's Manual Y0(3)
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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 re‐
63 turn 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 and an FE_DIVBYZERO exception is raised
81 (but see BUGS).
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 set to ERANGE (but see BUGS). An overflow floating-
89 point exception (FE_OVERFLOW) is raised.
90
92 For an explanation of the terms used in this section, see at‐
93 tributes(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 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 Before glibc 2.17, did not set errno for "range error: result under‐
115 flow".
116 In glibc version 2.3.2 and earlier, these functions do not raise an in‐
118 valid floating-point exception (FE_INVALID) when a domain error occurs.
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121 j0(3)
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124 This page is part of release 5.10 of the Linux man-pages project. A
125 description of the project, information about reporting bugs, and the
126 latest version of this page, can be found at
127 https://www.kernel.org/doc/man-pages/.
128 2020-06-09 Y0(3)