| .\" Copyright 1993 David Metcalfe (david@prism.demon.co.uk) |
| .\" and Copyright 2008, Linux Foundation, written by Michael Kerrisk |
| .\" <mtk.manpages@gmail.com> |
| .\" |
| .\" %%%LICENSE_START(VERBATIM) |
| .\" Permission is granted to make and distribute verbatim copies of this |
| .\" manual provided the copyright notice and this permission notice are |
| .\" preserved on all copies. |
| .\" |
| .\" Permission is granted to copy and distribute modified versions of this |
| .\" manual under the conditions for verbatim copying, provided that the |
| .\" entire resulting derived work is distributed under the terms of a |
| .\" permission notice identical to this one. |
| .\" |
| .\" Since the Linux kernel and libraries are constantly changing, this |
| .\" manual page may be incorrect or out-of-date. The author(s) assume no |
| .\" responsibility for errors or omissions, or for damages resulting from |
| .\" the use of the information contained herein. The author(s) may not |
| .\" have taken the same level of care in the production of this manual, |
| .\" which is licensed free of charge, as they might when working |
| .\" professionally. |
| .\" |
| .\" Formatted or processed versions of this manual, if unaccompanied by |
| .\" the source, must acknowledge the copyright and authors of this work. |
| .\" %%%LICENSE_END |
| .\" |
| .\" 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 2016-03-15 "" "Linux Programmer's Manual" |
| .SH NAME |
| y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl \- |
| Bessel functions of the second kind |
| .SH SYNOPSIS |
| .nf |
| .B #include <math.h> |
| .sp |
| .BI "double y0(double " x ); |
| .br |
| .BI "double y1(double " x ); |
| .br |
| .BI "double yn(int " n ", double " x ); |
| .sp |
| .BI "float y0f(float " x ); |
| .br |
| .BI "float y1f(float " x ); |
| .br |
| .BI "float ynf(int " n ", float " x ); |
| .sp |
| .BI "long double y0l(long double " x ); |
| .br |
| .BI "long double y1l(long double " x ); |
| .br |
| .BI "long double ynl(int " n ", long double " x ); |
| .fi |
| .sp |
| Link with \fI\-lm\fP. |
| .sp |
| .in -4n |
| Feature Test Macro Requirements for glibc (see |
| .BR feature_test_macros (7)): |
| .in |
| .sp |
| .ad l |
| .BR y0 (), |
| .BR y1 (), |
| .BR yn (): |
| .RS 4 |
| _XOPEN_SOURCE |
| || /* Since glibc 2.19: */ _DEFAULT_SOURCE |
| || /* Glibc versions <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE |
| .RE |
| .br |
| .BR y0f (), |
| .BR y0l (), |
| .BR y1f (), |
| .BR y1l (), |
| .BR ynf (), |
| .BR ynl (): |
| .RS 4 |
| _XOPEN_SOURCE \ >=\ 600 |
| || (_ISOC99_SOURCE && _XOPEN_SOURCE) |
| || /* Since glibc 2.19: */ _DEFAULT_SOURCE |
| || /* Glibc versions <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE |
| .RE |
| .ad b |
| .SH DESCRIPTION |
| .PP |
| 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 . |
| .PP |
| The value of |
| .I x |
| must be positive. |
| .PP |
| 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 . |
| |
| If |
| .I x |
| is a NaN, a NaN is returned. |
| |
| 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.) |
| |
| 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. |
| |
| 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 |
| .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. |
| .PP |
| 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 |
| .\" FIXME . y0(0.0) gives EDOM |
| .BR ERANGE |
| (but see BUGS). |
| No |
| .B FE_DIVBYZERO |
| exception is returned by |
| .BR fetestexcept (3) |
| for this case. |
| .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6808 |
| .TP |
| Range error: result underflow |
| .\" e.g., y0(1e33) on glibc 2.8/x86-32 |
| .I errno |
| is set to |
| .BR ERANGE . |
| .\" An underflow floating-point exception |
| .\" .RB ( FE_UNDERFLOW ) |
| .\" is raised. |
| .\" FIXME . Is it intentional that these functions do not use FE_*? |
| .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6806 |
| No |
| .B FE_UNDERFLOW |
| exception is returned by |
| .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 |
| .\" .BR ERANGE . |
| .I errno |
| is not set for this case. |
| .\" FIXME . Is it intentional that errno is not set? |
| .\" Bug raised: http://sources.redhat.com/bugzilla/show_bug.cgi?id=6808 |
| 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; |
| lb lb lb |
| l l l. |
| Interface Attribute Value |
| T{ |
| .BR y0 (), |
| .BR y0f (), |
| .BR y0l () |
| T} Thread safety MT-Safe |
| T{ |
| .BR y1 (), |
| .BR y1f (), |
| .BR y1l () |
| T} Thread safety MT-Safe |
| T{ |
| .BR yn (), |
| .BR ynf (), |
| .BR ynl () |
| T} Thread safety MT-Safe |
| .TE |
| .SH CONFORMING TO |
| The functions returning |
| .I double |
| conform to SVr4, 4.3BSD, |
| POSIX.1-2001, POSIX.1-2008. |
| The others are nonstandard functions that also exist on the BSDs. |
| .SH BUGS |
| On a pole error, these functions set |
| .I errno |
| to |
| .BR EDOM , |
| instead of |
| .BR ERANGE |
| as POSIX.1-2004 requires. |
| .\" FIXME . |
| .\" Bug raised: http://sourceware.org/bugzilla/show_bug.cgi?id=6807 |
| |
| In glibc version 2.3.2 and earlier, |
| .\" FIXME . Actually, 2.3.2 is the earliest test result I have; so yet |
| .\" to confirm if this error occurs only in 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) |