HP15c continued fraction for Ln(Gamma) « Next Oldest | Next Newest »

 ▼ Tom Grydeland Member Posts: 54 Threads: 13 Joined: Feb 2012 09-30-2013, 05:48 AM Hi all, In the "Advanced functions handbook" for the HP-15C, pages 65ff, there is a continued-fraction approximation for the function Ln(Gamma(x)). The first five terms of the expansion are given as fractions, the last two as decimal fractions. I've managed to track down the fractions that these decimals represent: a5 = 22,999/22,737 ~= 1.011523068126842 a6 = 29,944,523/19,733,142 ~= 1.517473649153287 I'm also struck by an oddity in the program. 6 is stored in the indirect register, and before the loop, a6 is recalled. As a result, the innermost fraction is a6/(x+a6). I'm not terribly familiar with continued fractions, but it looks suspicious to me. However, changing the initial value of the indirect register to 5 (meaning that the innermost fraction becomes a5/(x+a6) and the continued fraction one level smaller) changes the last digit in the real example -- Ln(Gamma(4.2)) -- and the value produced by the version in the book is correctly rounded in the last digit, when letting the WP-34S serve as reference. So, my question is: Is the example correct, and if so: why? A shout of "RTFM" is acceptable, if it is accompanied with a suggestion of how to find a version of the FM that explains how the CF can be evaluated, i.e. how one should begin. Thanks, --T

 Possibly Related Threads... Thread Author Replies Views Last Post HP Prime: Long integers (continued) Helge Gabert 2 734 11-07-2013, 11:24 AM Last Post: Helge Gabert HP Prime program: rounding to a fraction Patrice 3 824 10-31-2013, 06:16 AM Last Post: Joe Horn 1984 HP15C rattles Footloose (Illinois) 4 904 10-15-2013, 09:43 PM Last Post: BobVA HP Prime emulator: Gamma function Stephan Matthys 28 3,160 08-21-2013, 04:52 PM Last Post: Namir What is the Gamma approximation you use? Namir 21 2,438 08-05-2013, 07:14 AM Last Post: Namir SandMath routine of the week: Inverse Gamma Function Ángel Martin 39 4,295 03-24-2013, 08:19 AM Last Post: peacecalc HP15c LE emulator with unlimited number of activations Nick_S 23 2,896 01-24-2013, 03:59 PM Last Post: Victor Quiros battery test for the HP15c Limited Edition Guido (Canada) 3 788 01-03-2013, 08:17 AM Last Post: Jeff O. uRCL* on HP15C Csaba Tizedes (Hungary) 2 651 12-29-2012, 06:09 PM Last Post: Luiz C. Vieira (Brazil) New empirical fit for ln(x) Namir 0 403 12-11-2012, 12:49 PM Last Post: Namir

Forum Jump: