'\" et
.TH Y0 "3P" 2013 "IEEE/The Open Group" "POSIX Programmer's Manual"
.SH PROLOG
This manual page is part of the POSIX Programmer's Manual.
The Linux implementation of this interface may differ (consult
the corresponding Linux manual page for details of Linux behavior),
or the interface may not be implemented on Linux.

.SH NAME
y0,
y1,
yn
\(em Bessel functions of the second kind
.SH SYNOPSIS
.LP
.nf
#include <math.h>
.P
double y0(double \fIx\fP);
double y1(double \fIx\fP);
double yn(int \fIn\fP, double \fIx\fP);
.fi
.SH DESCRIPTION
The
\fIy0\fR(),
\fIy1\fR(),
and
\fIyn\fR()
functions shall compute Bessel functions of
.IR x
of the second kind of orders 0, 1, and
.IR n ,
respectively.
.P
An application wishing to check for error situations should set
.IR errno
to zero and call
.IR feclearexcept (FE_ALL_EXCEPT)
before calling these functions. On return, if
.IR errno
is non-zero or \fIfetestexcept\fR(FE_INVALID | FE_DIVBYZERO |
FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.
.SH "RETURN VALUE"
Upon successful completion, these functions shall return the relevant
Bessel value of
.IR x
of the second kind.
.P
If
.IR x
is NaN, NaN shall be returned.
.P
If the
.IR x
argument to these functions is negative, \(miHUGE_VAL or NaN shall be
returned, and a domain error may occur.
.P
If
.IR x
is 0.0, \(miHUGE_VAL shall be returned and a pole error may occur.
.P
If the correct result would cause underflow, 0.0 shall be returned and
a range error may occur.
.P
If the correct result would cause overflow, \(miHUGE_VAL or 0.0 shall
be returned and a range error may occur.
.SH ERRORS
These functions may fail if:
.IP "Domain\ Error" 12
The value of
.IR x
is negative.
.RS 12 
.P
If the integer expression (\fImath_errhandling\fR & MATH_ERRNO) is
non-zero, then
.IR errno
shall be set to
.BR [EDOM] .
If the integer expression (\fImath_errhandling\fR & MATH_ERREXCEPT) is
non-zero, then the invalid floating-point exception shall be raised.
.RE
.IP "Pole\ Error" 12
The value of
.IR x
is zero.
.RS 12 
.P
If the integer expression (\fImath_errhandling\fR & MATH_ERRNO) is
non-zero, then
.IR errno
shall be set to
.BR [ERANGE] .
If the integer expression (\fImath_errhandling\fR & MATH_ERREXCEPT) is
non-zero, then the divide-by-zero floating-point exception shall be
raised.
.RE
.IP "Range\ Error" 12
The correct result would cause overflow.
.RS 12 
.P
If the integer expression (\fImath_errhandling\fR & MATH_ERRNO) is
non-zero, then
.IR errno
shall be set to
.BR [ERANGE] .
If the integer expression (\fImath_errhandling\fR & MATH_ERREXCEPT) is
non-zero, then the overflow floating-point exception shall be raised.
.RE
.IP "Range\ Error" 12
The value of
.IR x
is too large in magnitude, or the correct result would cause
underflow.
.RS 12 
.P
If the integer expression (\fImath_errhandling\fR & MATH_ERRNO) is
non-zero, then
.IR errno
shall be set to
.BR [ERANGE] .
If the integer expression (\fImath_errhandling\fR & MATH_ERREXCEPT) is
non-zero, then the underflow floating-point exception shall be raised.
.RE
.LP
.IR "The following sections are informative."
.SH EXAMPLES
None.
.SH "APPLICATION USAGE"
On error, the expressions (\fImath_errhandling\fR & MATH_ERRNO) and
(\fImath_errhandling\fR & MATH_ERREXCEPT) are independent of each
other, but at least one of them must be non-zero.
.SH RATIONALE
None.
.SH "FUTURE DIRECTIONS"
None.
.SH "SEE ALSO"
.IR "\fIfeclearexcept\fR\^(\|)",
.IR "\fIfetestexcept\fR\^(\|)",
.IR "\fIisnan\fR\^(\|)",
.IR "\fIj0\fR\^(\|)"
.P
The Base Definitions volume of POSIX.1\(hy2008,
.IR "Section 4.19" ", " "Treatment of Error Conditions for Mathematical Functions",
.IR "\fB<math.h>\fP"
.SH COPYRIGHT
Portions of this text are reprinted and reproduced in electronic form
from IEEE Std 1003.1, 2013 Edition, Standard for Information Technology
-- Portable Operating System Interface (POSIX), The Open Group Base
Specifications Issue 7, Copyright (C) 2013 by the Institute of
Electrical and Electronics Engineers, Inc and The Open Group.
(This is POSIX.1-2008 with the 2013 Technical Corrigendum 1 applied.) In the
event of any discrepancy between this version and the original IEEE and
The Open Group Standard, the original IEEE and The Open Group Standard
is the referee document. The original Standard can be obtained online at
http://www.unix.org/online.html .

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