383 lines
6.6 KiB
HTML
383 lines
6.6 KiB
HTML
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
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<HTML><HEAD><TITLE>Man page of Y0</TITLE>
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</HEAD><BODY>
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<H1>Y0</H1>
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Section: Linux Programmer's Manual (3)<BR>Updated: 2017-09-15<BR><A HREF="#index">Index</A>
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<A HREF="/cgi-bin/man/man2html">Return to Main Contents</A><HR>
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<A NAME="lbAB"> </A>
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<H2>NAME</H2>
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y0, y0f, y0l, y1, y1f, y1l, yn, ynf, ynl -
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Bessel functions of the second kind
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<A NAME="lbAC"> </A>
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<H2>SYNOPSIS</H2>
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<PRE>
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<B>#include <<A HREF="file:///usr/include/math.h">math.h</A>></B>
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<B>double y0(double </B><I>x</I><B>);</B>
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<B>double y1(double </B><I>x</I><B>);</B>
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<B>double yn(int </B><I>n</I><B>, double </B><I>x</I><B>);</B>
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<B>float y0f(float </B><I>x</I><B>);</B>
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<B>float y1f(float </B><I>x</I><B>);</B>
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<B>float ynf(int </B><I>n</I><B>, float </B><I>x</I><B>);</B>
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<B>long double y0l(long double </B><I>x</I><B>);</B>
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<B>long double y1l(long double </B><I>x</I><B>);</B>
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<B>long double ynl(int </B><I>n</I><B>, long double </B><I>x</I><B>);</B>
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</PRE>
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<P>
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Link with <I>-lm</I>.
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<P>
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Feature Test Macro Requirements for glibc (see
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<B><A HREF="/cgi-bin/man/man2html?7+feature_test_macros">feature_test_macros</A></B>(7)):
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<P>
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<B>y0</B>(),
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<B>y1</B>(),
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<B>yn</B>():
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<DL COMPACT><DT id="1"><DD>
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_XOPEN_SOURCE
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<BR> || /* Since glibc 2.19: */ _DEFAULT_SOURCE
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<BR> || /* Glibc versions <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
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</DL>
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<BR>
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<B>y0f</B>(),
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<B>y0l</B>(),
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<B>y1f</B>(),
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<B>y1l</B>(),
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<B>ynf</B>(),
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<B>ynl</B>():
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<DL COMPACT><DT id="2"><DD>
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_XOPEN_SOURCE >= 600
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<BR> || (_ISOC99_SOURCE && _XOPEN_SOURCE)
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<BR> || /* Since glibc 2.19: */ _DEFAULT_SOURCE
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<BR> || /* Glibc versions <= 2.19: */ _SVID_SOURCE || _BSD_SOURCE
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</DL>
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<A NAME="lbAD"> </A>
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<H2>DESCRIPTION</H2>
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<P>
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The
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<B>y0</B>()
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and
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<B>y1</B>()
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functions return Bessel functions of
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<I>x</I>
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of the second kind of orders 0 and 1, respectively.
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The
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<B>yn</B>()
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function
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returns the Bessel function of
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<I>x</I>
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of the second kind of order
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<I>n</I>.
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<P>
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The value of
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<I>x</I>
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must be positive.
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<P>
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The
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<B>y0f</B>(),
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<B>y1f</B>(),
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and
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<B>ynf</B>()
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functions are versions that take and return
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<I>float</I>
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values.
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The
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<B>y0l</B>(),
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<B>y1l</B>(),
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and
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<B>ynl</B>()
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functions are versions that take and return
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<I>long double</I>
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values.
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<A NAME="lbAE"> </A>
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<H2>RETURN VALUE</H2>
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On success, these functions return the appropriate
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Bessel value of the second kind for
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<I>x</I>.
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<P>
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If
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<I>x</I>
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is a NaN, a NaN is returned.
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<P>
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If
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<I>x</I>
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is negative,
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a domain error occurs,
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and the functions return
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-<B>HUGE_VAL</B>,
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-<B>HUGE_VALF</B>,
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or
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-<B>HUGE_VALL</B>,
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respectively.
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(POSIX.1-2001 also allows a NaN return for this case.)
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<P>
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If
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<I>x</I>
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is 0.0,
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a pole error occurs,
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and the functions return
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-<B>HUGE_VAL</B>,
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-<B>HUGE_VALF</B>,
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or
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-<B>HUGE_VALL</B>,
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respectively.
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<P>
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If the result underflows,
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a range error occurs,
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and the functions return 0.0
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<P>
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If the result overflows,
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a range error occurs,
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and the functions return
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-<B>HUGE_VAL</B>,
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-<B>HUGE_VALF</B>,
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or
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-<B>HUGE_VALL</B>,
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respectively.
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(POSIX.1-2001 also allows a 0.0 return for this case.)
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<A NAME="lbAF"> </A>
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<H2>ERRORS</H2>
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See
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<B><A HREF="/cgi-bin/man/man2html?7+math_error">math_error</A></B>(7)
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for information on how to determine whether an error has occurred
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when calling these functions.
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<P>
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The following errors can occur:
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<DL COMPACT>
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<DT id="3">Domain error: <I>x</I> is negative<DD>
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<I>errno</I>
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is set to
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<B>EDOM</B>.
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An invalid floating-point exception
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(<B>FE_INVALID</B>)
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is raised.
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<DT id="4">Pole error: <I>x</I> is 0.0<DD>
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<I>errno</I>
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is set to
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<B>ERANGE</B>
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(but see BUGS).
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No
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<B>FE_DIVBYZERO</B>
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exception is returned by
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<B><A HREF="/cgi-bin/man/man2html?3+fetestexcept">fetestexcept</A></B>(3)
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for this case.
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<DT id="5">Range error: result underflow<DD>
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<I>errno</I>
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is set to
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<B>ERANGE</B>.
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No
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<B>FE_UNDERFLOW</B>
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exception is returned by
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<B><A HREF="/cgi-bin/man/man2html?3+fetestexcept">fetestexcept</A></B>(3)
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for this case.
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<DT id="6">Range error: result overflow<DD>
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<I>errno</I>
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is not set for this case.
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An overflow floating-point exception
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(<B>FE_OVERFLOW</B>)
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is raised.
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</DL>
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<A NAME="lbAG"> </A>
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<H2>ATTRIBUTES</H2>
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For an explanation of the terms used in this section, see
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<B><A HREF="/cgi-bin/man/man2html?7+attributes">attributes</A></B>(7).
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<TABLE BORDER>
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<TR VALIGN=top><TD><B>Interface</B></TD><TD><B>Attribute</B></TD><TD><B>Value</B><BR></TD></TR>
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<TR VALIGN=top><TD>
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<B>y0</B>(),
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<B>y0f</B>(),
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<B>y0l</B>()
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</TD><TD>Thread safety</TD><TD>MT-Safe<BR></TD></TR>
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<TR VALIGN=top><TD>
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<B>y1</B>(),
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<B>y1f</B>(),
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<B>y1l</B>()
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</TD><TD>Thread safety</TD><TD>MT-Safe<BR></TD></TR>
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<TR VALIGN=top><TD>
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<B>yn</B>(),
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<B>ynf</B>(),
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<B>ynl</B>()
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</TD><TD>Thread safety</TD><TD>MT-Safe<BR></TD></TR>
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</TABLE>
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<A NAME="lbAH"> </A>
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<H2>CONFORMING TO</H2>
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The functions returning
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<I>double</I>
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conform to SVr4, 4.3BSD,
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POSIX.1-2001, POSIX.1-2008.
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The others are nonstandard functions that also exist on the BSDs.
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<A NAME="lbAI"> </A>
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<H2>BUGS</H2>
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On a pole error, these functions set
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<I>errno</I>
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to
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<B>EDOM</B>,
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instead of
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<B>ERANGE</B>
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as POSIX.1-2004 requires.
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<P>
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In glibc version 2.3.2 and earlier,
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these functions do not raise an invalid floating-point exception
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(<B>FE_INVALID</B>)
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when a domain error occurs.
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<A NAME="lbAJ"> </A>
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<H2>SEE ALSO</H2>
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<B><A HREF="/cgi-bin/man/man2html?3+j0">j0</A></B>(3)
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<A NAME="lbAK"> </A>
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<H2>COLOPHON</H2>
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This page is part of release 5.05 of the Linux
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<I>man-pages</I>
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project.
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A description of the project,
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information about reporting bugs,
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and the latest version of this page,
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can be found at
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<A HREF="https://www.kernel.org/doc/man-pages/.">https://www.kernel.org/doc/man-pages/.</A>
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<P>
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<HR>
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<A NAME="index"> </A><H2>Index</H2>
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<DL>
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<DT id="7"><A HREF="#lbAB">NAME</A><DD>
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<DT id="8"><A HREF="#lbAC">SYNOPSIS</A><DD>
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<DT id="9"><A HREF="#lbAD">DESCRIPTION</A><DD>
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<DT id="10"><A HREF="#lbAE">RETURN VALUE</A><DD>
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<DT id="11"><A HREF="#lbAF">ERRORS</A><DD>
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<DT id="12"><A HREF="#lbAG">ATTRIBUTES</A><DD>
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<DT id="13"><A HREF="#lbAH">CONFORMING TO</A><DD>
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<DT id="14"><A HREF="#lbAI">BUGS</A><DD>
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<DT id="15"><A HREF="#lbAJ">SEE ALSO</A><DD>
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<DT id="16"><A HREF="#lbAK">COLOPHON</A><DD>
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</DL>
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<HR>
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This document was created by
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<A HREF="/cgi-bin/man/man2html">man2html</A>,
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using the manual pages.<BR>
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Time: 00:06:01 GMT, March 31, 2021
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