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-'\" t
-.\" Copyright 1993 David Metcalfe (david@prism.demon.co.uk)
-.\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk
-.\" <mtk.manpages@gmail.com>
-.\"
-.\" SPDX-License-Identifier: Linux-man-pages-copyleft
-.\"
-.\" References consulted:
-.\" Linux libc source code
-.\" Lewine's _POSIX Programmer's Guide_ (O'Reilly & Associates, 1991)
-.\" 386BSD man pages
-.\" Modified Sat Jul 24 19:08:17 1993 by Rik Faith (faith@cs.unc.edu)
-.\" Modified 2002-08-25, aeb
-.\" Modified 2004-11-12 as per suggestion by Fabian Kreutz/AEB
-.\" 2008-07-24, mtk, created this page, based on material from j0.3.
-.\"
-.TH y0 3 2023-10-31 "Linux man-pages 6.7"
-.SH NAME
-y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl \-
-Bessel functions of the second kind
-.SH LIBRARY
-Math library
-.RI ( libm ", " \-lm )
-.SH SYNOPSIS
-.nf
-.B #include <math.h>
-.P
-.BI "double y0(double " x );
-.BI "double y1(double " x );
-.BI "double yn(int " n ", double " x );
-.P
-.BI "float y0f(float " x );
-.BI "float y1f(float " x );
-.BI "float ynf(int " n ", float " x );
-.P
-.BI "long double y0l(long double " x );
-.BI "long double y1l(long double " x );
-.BI "long double ynl(int " n ", long double " x );
-.fi
-.P
-.RS -4
-Feature Test Macro Requirements for glibc (see
-.BR feature_test_macros (7)):
-.RE
-.P
-.BR y0 (),
-.BR y1 (),
-.BR yn ():
-.nf
- _XOPEN_SOURCE
- || /* Since glibc 2.19: */ _DEFAULT_SOURCE
- || /* glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
-.fi
-.P
-.BR y0f (),
-.BR y0l (),
-.BR y1f (),
-.BR y1l (),
-.BR ynf (),
-.BR ynl ():
-.nf
- _XOPEN_SOURCE >= 600
- || (_ISOC99_SOURCE && _XOPEN_SOURCE)
- || /* Since glibc 2.19: */ _DEFAULT_SOURCE
- || /* glibc <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
-.fi
-.SH DESCRIPTION
-The
-.BR y0 ()
-and
-.BR y1 ()
-functions return Bessel functions of
-.I x
-of the second kind of orders 0 and 1, respectively.
-The
-.BR yn ()
-function
-returns the Bessel function of
-.I x
-of the second kind of order
-.IR n .
-.P
-The value of
-.I x
-must be positive.
-.P
-The
-.BR y0f (),
-.BR y1f (),
-and
-.BR ynf ()
-functions are versions that take and return
-.I float
-values.
-The
-.BR y0l (),
-.BR y1l (),
-and
-.BR ynl ()
-functions are versions that take and return
-.I "long double"
-values.
-.SH RETURN VALUE
-On success, these functions return the appropriate
-Bessel value of the second kind for
-.IR x .
-.P
-If
-.I x
-is a NaN, a NaN is returned.
-.P
-If
-.I x
-is negative,
-a domain error occurs,
-and the functions return
-.RB \- HUGE_VAL ,
-.RB \- HUGE_VALF ,
-or
-.RB \- HUGE_VALL ,
-respectively.
-(POSIX.1-2001 also allows a NaN return for this case.)
-.P
-If
-.I x
-is 0.0,
-a pole error occurs,
-and the functions return
-.RB \- HUGE_VAL ,
-.RB \- HUGE_VALF ,
-or
-.RB \- HUGE_VALL ,
-respectively.
-.P
-If the result underflows,
-a range error occurs,
-and the functions return 0.0
-.P
-If the result overflows,
-a range error occurs,
-and the functions return
-.RB \- HUGE_VAL ,
-.RB \- HUGE_VALF ,
-or
-.RB \- HUGE_VALL ,
-respectively.
-(POSIX.1-2001 also allows a 0.0 return for this case.)
-.SH ERRORS
-See
-.BR math_error (7)
-for information on how to determine whether an error has occurred
-when calling these functions.
-.P
-The following errors can occur:
-.TP
-Domain error: \fIx\fP is negative
-.I errno
-is set to
-.BR EDOM .
-An invalid floating-point exception
-.RB ( FE_INVALID )
-is raised.
-.TP
-Pole error: \fIx\fP is 0.0
-.\" Before POSIX.1-2001 TC2, this was (inconsistently) specified
-.\" as a range error.
-.I errno
-is set to
-.B ERANGE
-and an
-.B FE_DIVBYZERO
-exception is raised
-(but see BUGS).
-.TP
-Range error: result underflow
-.\" e.g., y0(1e33) on glibc 2.8/x86-32
-.I errno
-is set to
-.BR ERANGE .
-No
-.B FE_UNDERFLOW
-exception is returned by
-.\" This is intended behavior
-.\" See https://www.sourceware.org/bugzilla/show_bug.cgi?id=6806
-.BR fetestexcept (3)
-for this case.
-.TP
-Range error: result overflow
-.\" e.g., yn(10, 1e-40) on glibc 2.8/x86-32
-.I errno
-is set to
-.B ERANGE
-(but see BUGS).
-An overflow floating-point exception
-.RB ( FE_OVERFLOW )
-is raised.
-.SH ATTRIBUTES
-For an explanation of the terms used in this section, see
-.BR attributes (7).
-.TS
-allbox;
-lbx lb lb
-l l l.
-Interface Attribute Value
-T{
-.na
-.nh
-.BR y0 (),
-.BR y0f (),
-.BR y0l ()
-T} Thread safety MT-Safe
-T{
-.na
-.nh
-.BR y1 (),
-.BR y1f (),
-.BR y1l ()
-T} Thread safety MT-Safe
-T{
-.na
-.nh
-.BR yn (),
-.BR ynf (),
-.BR ynl ()
-T} Thread safety MT-Safe
-.TE
-.SH STANDARDS
-.TP
-.BR y0 ()
-.TQ
-.BR y1 ()
-.TQ
-.BR yn ()
-POSIX.1-2008.
-.TP
-Others:
-BSD.
-.SH HISTORY
-.TP
-.BR y0 ()
-.TQ
-.BR y1 ()
-.TQ
-.BR yn ()
-SVr4, 4.3BSD,
-POSIX.1-2001.
-.TP
-Others:
-BSD.
-.SH BUGS
-Before glibc 2.19,
-.\" http://sourceware.org/bugzilla/show_bug.cgi?id=6807
-these functions misdiagnosed pole errors:
-.I errno
-was set to
-.BR EDOM ,
-instead of
-.B ERANGE
-and no
-.B FE_DIVBYZERO
-exception was raised.
-.P
-Before glibc 2.17,
-.\" https://www.sourceware.org/bugzilla/show_bug.cgi?id=6808
-did not set
-.I errno
-for "range error: result underflow".
-.P
-In glibc 2.3.2 and earlier,
-.\" Actually, 2.3.2 is the earliest test result I have; so yet
-.\" to confirm if this error occurs only in glibc 2.3.2.
-these functions do not raise an invalid floating-point exception
-.RB ( FE_INVALID )
-when a domain error occurs.
-.SH SEE ALSO
-.BR j0 (3)