функции Бесселя второго рода (Bessel functions of the second kind)
Имя (Name)
y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl - Bessel functions of
the second kind
Синопсис (Synopsis)
#include <math.h>
double y0(double x);
double y1(double x);
double yn(int n, double x);
float y0f(float x);
float y1f(float x);
float ynf(int n, float x);
long double y0l(long double x);
long double y1l(long double x);
long double ynl(int n, long double x);
Link with -lm.
Feature Test Macro Requirements for glibc (see
feature_test_macros(7)):
y0(), y1(), yn():
_XOPEN_SOURCE
|| /* Since glibc 2.19: */ _DEFAULT_SOURCE
|| /* Glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
y0f(), y0l(), y1f(), y1l(), ynf(), ynl():
_XOPEN_SOURCE >= 600
|| (_ISOC99_SOURCE && _XOPEN_SOURCE)
|| /* Since glibc 2.19: */ _DEFAULT_SOURCE
|| /* Glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
Описание (Description)
The y0() and y1() functions return Bessel functions of x of the
second kind of orders 0 and 1, respectively. The yn() function
returns the Bessel function of x of the second kind of order n.
The value of x must be positive.
The y0f(), y1f(), and ynf() functions are versions that take and
return float values. The y0l(), y1l(), and ynl() functions are
versions that take and return long double values.
Возвращаемое значение (Return value)
On success, these functions return the appropriate Bessel value
of the second kind for x.
If x is a NaN, a NaN is returned.
If x is negative, a domain error occurs, and the functions return
-HUGE_VAL, -HUGE_VALF, or -HUGE_VALL, respectively.
(POSIX.1-2001 also allows a NaN return for this case.)
If x is 0.0, a pole error occurs, and the functions return
-HUGE_VAL, -HUGE_VALF, or -HUGE_VALL, respectively.
If the result underflows, a range error occurs, and the functions
return 0.0
If the result overflows, a range error occurs, and the functions
return -HUGE_VAL, -HUGE_VALF, or -HUGE_VALL, respectively.
(POSIX.1-2001 also allows a 0.0 return for this case.)
Ошибки (Error)
See math_error(7) for information on how to determine whether an
error has occurred when calling these functions.
The following errors can occur:
Domain error: x is negative
errno is set to EDOM. An invalid floating-point exception
(FE_INVALID) is raised.
Pole error: x is 0.0
errno is set to ERANGE and an FE_DIVBYZERO exception is
raised (but see BUGS).
Range error: result underflow
errno is set to ERANGE. No FE_UNDERFLOW exception is
returned by fetestexcept(3) for this case.
Range error: result overflow
errno is set to ERANGE (but see BUGS). An overflow
floating-point exception (FE_OVERFLOW) is raised.
Атрибуты (Attributes)
For an explanation of the terms used in this section, see
attributes(7).
┌──────────────────────────────────────┬───────────────┬─────────┐
│Interface │ Attribute │ Value │
├──────────────────────────────────────┼───────────────┼─────────┤
│y0(), y0f(), y0l() │ Thread safety │ MT-Safe │
├──────────────────────────────────────┼───────────────┼─────────┤
│y1(), y1f(), y1l() │ Thread safety │ MT-Safe │
├──────────────────────────────────────┼───────────────┼─────────┤
│yn(), ynf(), ynl() │ Thread safety │ MT-Safe │
└──────────────────────────────────────┴───────────────┴─────────┘
Стандарты (Conforming to)
The functions returning double conform to SVr4, 4.3BSD,
POSIX.1-2001, POSIX.1-2008. The others are nonstandard functions
that also exist on the BSDs.
Ошибки (баги) (Bugs)
Before glibc 2.19, these functions misdiagnosed pole errors:
errno was set to EDOM, instead of ERANGE and no FE_DIVBYZERO
exception was raised.
Before glibc 2.17, did not set errno for "range error: result
underflow".
In glibc version 2.3.2 and earlier, these functions do not raise
an invalid floating-point exception (FE_INVALID) when a domain
error occurs.
Смотри также (See also)
j0(3)
