http://www.mapleprimes.com/posts/41570-C-Code-For-The-Hypergeometric-Function en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Wed, 10 Jun 2026 05:14:54 GMT Wed, 10 Jun 2026 05:14:54 GMT The latest comments added to the Post, C code for the hypergeometric function 2F1 using an idea of Gosper http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/posts/41570-C-Code-For-The-Hypergeometric-Function http://www.mapleprimes.com/posts/41570-C-Code-For-The-Hypergeometric-Function?ref=Feed:MaplePrimes:C code for the hypergeometric function 2F1 using an idea of Gosper:Comments#comment77527 This is the kind of stuff where Maple is a real life-saver. Most mortals cannot manipulate that many symbols (correctly) in finite time! Question: do you have any intuition at all for where that 3-variable recurrence comes from? [I did not look at Forrey's article]. The inner 2-variable coupled recurrence is rather intriguing. The latest comments added to the Post, C code for the hypergeometric function 2F1 using an idea of Gosper 77527 Mon, 09 Apr 2007 18:38:00 Z JacquesC JacquesC http://www.mapleprimes.com/posts/41570-C-Code-For-The-Hypergeometric-Function?ref=Feed:MaplePrimes:C code for the hypergeometric function 2F1 using an idea of Gosper:Comments#comment85696 :-) Actually I do not know ... Bill Gosper has a large herd of matrix recursions ... But I guess it comes through the quadratic transformation by looking at the terms. And the closed curve should be the pre-image where the transformed series converges (ok, the boundary, which is the unit circle). But I have not tried it seriously :-( And he has some similar for the exceptional cases (Problem 2 in the link). Forrey is just for reference, he uses the classical linear transformations and his very point is to use careful finite differences for the exceptional cases (or close to them). However I think it is difficult to cover all the complex plane (example: unit circle intersecting diagonals), I think there are notes by Temme on that. But so far Forrey seems to have the best know (public, double precision) code, Temme occasionally stated that at the num analysis usenet group. So it is a good reference. The latest comments added to the Post, C code for the hypergeometric function 2F1 using an idea of Gosper 85696 Mon, 09 Apr 2007 19:27:53 Z Axel Vogt Axel Vogt http://www.mapleprimes.com/posts/41570-C-Code-For-The-Hypergeometric-Function?ref=Feed:MaplePrimes:C code for the hypergeometric function 2F1 using an idea of Gosper:Comments#comment91325 yes, Temme sketches the problem of evaluating through power series and linear transformations in a (public available) lecture "Numerics of Special Functions" (2005) on pages 55 ff. The latest comments added to the Post, C code for the hypergeometric function 2F1 using an idea of Gosper 91325 Tue, 10 Apr 2007 00:19:34 Z Axel Vogt Axel Vogt http://www.mapleprimes.com/posts/41570-C-Code-For-The-Hypergeometric-Function?ref=Feed:MaplePrimes:C code for the hypergeometric function 2F1 using an idea of Gosper:Comments#comment91326 Is this herd available somewhere? If I have some time one day, I'll try to derive where that matrix recursion comes from. Yes, it indeed has to come from the quadratic transformation of the hypergeometric, but that's still pretty vague! The latest comments added to the Post, C code for the hypergeometric function 2F1 using an idea of Gosper 91326 Tue, 10 Apr 2007 02:11:35 Z JacquesC JacquesC http://www.mapleprimes.com/posts/41570-C-Code-For-The-Hypergeometric-Function?ref=Feed:MaplePrimes:C code for the hypergeometric function 2F1 using an idea of Gosper:Comments#comment77463 Uploaded a new version for the source code (correcting a bug and now the zip contains an Excel sheet as well, I forgot that). The herd ... not aware that it is visible in public but the sheppard is quite open minded and friendly. <a href='http://www.mapleprimes.com/files/102_hyp2f1_simple(16 Apr 2007).zip'>Download 102_hyp2f1_simple(16 Apr 2007).zip</a><br/><a href='http://www.mapleprimes.com/viewfile/1477'>View file details</a> The latest comments added to the Post, C code for the hypergeometric function 2F1 using an idea of Gosper 77463 Tue, 17 Apr 2007 00:43:20 Z Axel Vogt Axel Vogt http://www.mapleprimes.com/posts/41570-C-Code-For-The-Hypergeometric-Function?ref=Feed:MaplePrimes:C code for the hypergeometric function 2F1 using an idea of Gosper:Comments#comment74185 Dear Alex, I am very gratefull for the C code you have posted. The only issue I still have is that Gosper implementation does not always work due to probably limited precision. The set of parameters for which it fails is the following: a = 15.707313816165103 b = 20.981233738918458 c = 16.707313816165104 z = -1.8610000000000013 Gosper_2F1 returns: result = -6.5559386647252389e-009 while true answer according to Wolfram must be: 1.27029 10-9 Is there workaround for this type of issues. Is the real problem with (a-c) being negative integer? Thank you --ignat The latest comments added to the Post, C code for the hypergeometric function 2F1 using an idea of Gosper 74185 Sat, 05 Jan 2008 06:30:24 Z ishilov ishilov