1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Hypergeometric References</title> 5<link rel="stylesheet" href="../../math.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../../index.html" title="Math Toolkit 2.12.0"> 8<link rel="up" href="../hypergeometric.html" title="Hypergeometric Functions"> 9<link rel="prev" href="hypergeometric_pfq.html" title="Hypergeometric pFq"> 10<link rel="next" href="../powers.html" title="Basic Functions"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> 15<td align="center"><a href="../../../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<a accesskey="p" href="hypergeometric_pfq.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../hypergeometric.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../powers.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h3 class="title"> 27<a name="math_toolkit.hypergeometric.hypergeometric_refs"></a><a class="link" href="hypergeometric_refs.html" title="Hypergeometric References">Hypergeometric 28 References</a> 29</h3></div></div></div> 30<div class="orderedlist"><ol class="orderedlist" type="1"> 31<li class="listitem"> 32 Beals, Richard, and Roderick Wong. <span class="emphasis"><em>Special functions: a graduate 33 text.</em></span> Vol. 126. Cambridge University Press, 2010. 34 </li> 35<li class="listitem"> 36 Pearson, John W., Sheehan Olver, and Mason A. Porter. <span class="emphasis"><em>Numerical 37 methods for the computation of the confluent and Gauss hypergeometric 38 functions.</em></span> Numerical Algorithms 74.3 (2017): 821-866. 39 </li> 40<li class="listitem"> 41 Luke, Yudell L. <span class="emphasis"><em>Algorithms for Rational Approximations for 42 a Confluent Hypergeometric Function II.</em></span> MISSOURI UNIV KANSAS 43 CITY DEPT OF MATHEMATICS, 1976. 44 </li> 45<li class="listitem"> 46 Derezinski, Jan. <span class="emphasis"><em>Hypergeometric type functions and their symmetries.</em></span> 47 Annales Henri Poincaré. Vol. 15. No. 8. Springer Basel, 2014. 48 </li> 49<li class="listitem"> 50 Keith E. Muller <span class="emphasis"><em>Computing the confluent hypergeometric function, 51 M(a, b, x)</em></span>. Numer. Math. 90: 179-196 (2001). 52 </li> 53<li class="listitem"> 54 Carlo Morosi, Livio Pizzocchero. <span class="emphasis"><em>On the expansion of the Kummer 55 function in terms of incomplete Gamma functions.</em></span> Arch. Inequal. 56 Appl. 2 (2004), 49-72. 57 </li> 58<li class="listitem"> 59 Jose Luis Lopez, Nico M. Temme. <span class="emphasis"><em>Asymptotics and numerics of 60 polynomials used in Tricomi and Buchholz expansions of Kummer functions</em></span>. 61 Numerische Mathematik, August 2010. 62 </li> 63<li class="listitem"> 64 Javier Sesma. <span class="emphasis"><em>The Temme's sum rule for confluent hypergeometric 65 functions revisited</em></span>. Journal of Computational and Applied 66 Mathematics 163 (2004) 429-431. 67 </li> 68<li class="listitem"> 69 Javier Segura, Nico M. Temme. <span class="emphasis"><em>Numerically satisfactory solutions 70 of Kummer recurrence relations</em></span>. Numer. Math. (2008) 111:109-119. 71 </li> 72<li class="listitem"> 73 Alfredo Deano, Javier Segura. <span class="emphasis"><em>Transitory Minimal Solutions 74 Of Hypergeometric Recursions And Pseudoconvergence of Associated Continued 75 Fractions</em></span>. Mathematics of Computation, Volume 76, Number 258, 76 April 2007. 77 </li> 78<li class="listitem"> 79 W. Gautschi. <span class="emphasis"><em>Computational aspects of three-term recurrence 80 relations</em></span>. SIAM Review 9, no.1 (1967) 24-82. 81 </li> 82<li class="listitem"> 83 W. Gautschi. <span class="emphasis"><em>Anomalous convergence of a continued fraction 84 for ratios of Kummer functions</em></span>. Math. Comput., 31, no.140 85 (1977) 994-999. 86 </li> 87<li class="listitem"> 88 British Association for the Advancement of Science: <span class="emphasis"><em>Bessel 89 functions, Part II, Mathematical Tables vol. X</em></span>. Cambridge 90 (1952). 91 </li> 92</ol></div> 93</div> 94<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 95<td align="left"></td> 96<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 97 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 98 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 99 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 100 Daryle Walker and Xiaogang Zhang<p> 101 Distributed under the Boost Software License, Version 1.0. (See accompanying 102 file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) 103 </p> 104</div></td> 105</tr></table> 106<hr> 107<div class="spirit-nav"> 108<a accesskey="p" href="hypergeometric_pfq.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../hypergeometric.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../powers.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 109</div> 110</body> 111</html> 112