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Version:
4.4.5.dfsg-3ubuntu2 ▾
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<HTML>
<HEAD>
<TITLE>Hypergeometric function</TITLE>
</HEAD>
<BODY bgcolor="#FFFFFF" fgcolor="#000000">
<P><A NAME="gamma"></A>
<font size="+3" color="green"><B>Hypergeometric <sub>2</sub><i>F</i><sub>1</sub> function</B></font></P>
<P>
<TABLE border="1" cols="2" frame="box" rules="all" width="572">
<TR>
<TD width="15%" valign="top"><B>Syntax</B>:</TD>
<TD width="85%"><CODE>
y = HYPGEO(a,b,c,x)<BR />
y = CHLOGU(a,b,x)</CODE>
</TD></TR>
</table></p>
<p>
The hypergeometric function is also called the Gauss series.</P>
<P><IMG ALIGN="BOTTOM" SRC="hypgeoI01.png"></P>
<p>
The logarithmic confluent hypergeometric function:
<P><IMG ALIGN="BOTTOM" SRC="hypgeoI02.png"></P>
<p>
Where <IMG ALIGN="top" SRC="hypgeoI03.png"> is Kummer's function, or the
regular confluent hypergeometric function:
<P><IMG ALIGN="BOTTOM" SRC="hypgeoI04.png"></P>
<p>
where <IMG ALIGN="top" SRC="hypgeoI05.png"> and
<IMG ALIGN="top" SRC="hypgeoI06.png">
<p>
Note that this function fails when <IMG ALIGN="BOTTOM" SRC="hypgeoI07.png">
is close to zero for small <IMG ALIGN="BOTTOM" SRC="hypgeoI08.png">.
</BODY>
</HTML>