yn(3) - f14

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
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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(): _SVID_SOURCE || _BSD_SOURCE || _XOPEN_SOURCE
29       y0f(), y0l(), y1f(), y1l(), ynf(), ynl(): _SVID_SOURCE || _BSD_SOURCE
30       || _XOPEN_SOURCE >= 600
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DESCRIPTION

33       The  y0() and y1() functions return Bessel functions of x of the second
34       kind of orders 0 and 1, respectively.  The yn()  function  returns  the
35       Bessel function of x of the second kind of order n.
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37       The value of x must be positive.
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39       The  y0f()  etc.  and  y0l()  etc. functions are versions that take and
40       return float and long double values, respectively.
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RETURN VALUE

43       On success, these functions return the appropriate Bessel value of  the
44       second kind for x.
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46       If x is a NaN, a NaN is returned.
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48       If  x  is  negative,  a  domain  error occurs, and the functions return
49       -HUGE_VAL, -HUGE_VALF, or -HUGE_VALL, respectively.  (POSIX.1-2001 also
50       allows a NaN return for this case.)
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52       If  x  is 0.0, a pole error occurs, and the functions return -HUGE_VAL,
53       -HUGE_VALF, or -HUGE_VALL, respectively.
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55       If the result underflows, a  range  error  occurs,  and  the  functions
56       return 0.0
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58       If the result overflows, a range error occurs, and the functions return
59       -HUGE_VAL, -HUGE_VALF, or -HUGE_VALL, respectively.  (POSIX.1-2001 also
60       allows a 0.0 return for this case.)
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ERRORS

63       See  math_error(7) for information on how to determine whether an error
64       has occurred when calling these functions.
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66       The following errors can occur:
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68       Domain error: x is negative
69              errno is set  to  EDOM.   An  invalid  floating-point  exception
70              (FE_INVALID) is raised.
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72       Pole error: x is 0.0
73              errno  is  set to ERANGE (but see BUGS).  No FE_DIVBYZERO excep‐
74              tion is returned by fetestexcept(3) for this case.
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76       Range error: result underflow
77              errno is set to ERANGE.  No FE_UNDERFLOW exception  is  returned
78              by fetestexcept(3) for this case.
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80       Range error: result overflow
81              errno  is  not  set  for  this case.  An overflow floating-point
82              exception (FE_OVERFLOW) is raised.
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CONFORMING TO

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

89       On  a  pole error, these functions set errno to EDOM, instead of ERANGE
90       as POSIX.1-2004 requires.
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92       In glibc version 2.3.2 and earlier, these functions  do  not  raise  an
93       invalid  floating-point  exception  (FE_INVALID)  when  a  domain error
94       occurs.
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COLOPHON

100       This page is part of release 3.25 of the Linux  man-pages  project.   A
101       description  of  the project, and information about reporting bugs, can
102       be found at http://www.kernel.org/doc/man-pages/.
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106                                  2008-08-10                             Y0(3)