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| From | jacob navia <jacob@spamsink.net> |
|---|---|
| Newsgroups | comp.lang.c |
| Subject | Re: Euler's constant |
| Date | 2011-11-21 12:45 +0100 |
| Organization | lccwin |
| Message-ID | <jaddl0$eb6$1@speranza.aioe.org> (permalink) |
| References | <24357587.77.1321816326271.JavaMail.geo-discussion-forums@prnv30> |
Le 20/11/11 20:12, 88888 Dihedral a écrit :
> PROBLEM 1: COMPUTE THE EULER'S NUMBER UP TO 30 DIGITS AFTER 1.
> THE DIGIT REQUIRED SHOULD BE PARAMETER BY THE CALLER!
Euler's constant is the limit of the sum when N goes to infinity of:
1 + 1/2 + 1/3 + 1/4 + ... 1/N - ln(n)
This is related to the PSI function (digamma) by
Euler constant = -psi(1)
This can be calculated in C with this program:
(Using lcc-win. Other compilers will be able to do this too
but in a different way)
d:\lcc\mc79\test>type teuler.c
#include <qfloat.h>
#include <specialfns.h>
#include <stdio.h>
int main(void)
{
qfloat e=psiq(1.0q);
printf("Euler constant is:\n%.95qf\n",-e);
}
OUTPUT:
Euler constant is:
+0.577215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291747
Thanks to this poster I have uncovered a bug in that function, that I
could correct.
lcc-win uses the Cephes Mathematical library of Stephen L Moshier. He uses:
*
* d +-
* psi(x) = -- ln | (x)
* dx
*
* is the logarithmic derivative of the gamma function.
* For general positive x, the argument is made greater than 16
* using the recurrence psi(x+1) = psi(x) + 1/x.
* Then the following asymptotic expansion is applied:
*
* inf. B
* - 2k
* psi(x) = log(x) - 1/2x - > -------
* - 2k
* k=1 2k x
*
* where the B2k are Bernoulli numbers.
*
* psi(-x) = psi(x+1) + pi/tan(pi(x+1))
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OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! 88888 Dihedral <dihedral88888@googlemail.com> - 2011-11-20 11:12 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Ian Collins <ian-news@hotmail.com> - 2011-11-21 08:18 +1300
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Vincenzo Mercuri <vincenzo.mercuri@yahoo.it> - 2011-11-20 20:22 +0100
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! 88888 Dihedral <dihedral88888@googlemail.com> - 2011-11-20 11:23 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-11-20 15:03 -0500
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Kaz Kylheku <kaz@kylheku.com> - 2011-11-20 20:06 +0000
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! 88888 Dihedral <dihedral88888@googlemail.com> - 2011-11-20 12:13 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Ian Collins <ian-news@hotmail.com> - 2011-11-21 09:16 +1300
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Eric Sosman <esosman@ieee-dot-org.invalid> - 2011-11-20 15:37 -0500
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Joe Pfeiffer <pfeiffer@cs.nmsu.edu> - 2011-11-20 14:15 -0700
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Lew Pitcher <lpitcher@teksavvy.com> - 2011-11-20 13:45 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Malcolm McLean <malcolm.mclean5@btinternet.com> - 2011-11-21 00:44 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Phil Carmody <thefatphil_demunged@yahoo.co.uk> - 2011-11-21 12:44 +0200
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Lew Pitcher <lpitcher@teksavvy.com> - 2011-11-21 10:41 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! 88888 Dihedral <dihedral88888@googlemail.com> - 2011-11-21 00:53 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! "io_x" <a@b.c.invalid> - 2011-11-24 19:08 +0100
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Martin Ambuhl <mambuhl@earthlink.net> - 2011-11-20 17:32 -0500
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Keith Thompson <kst-u@mib.org> - 2011-11-20 14:55 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! 88888 Dihedral <dihedral88888@googlemail.com> - 2011-11-20 16:54 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Keith Thompson <kst-u@mib.org> - 2011-11-20 19:35 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Nick Keighley <nick_keighley_nospam@hotmail.com> - 2011-11-22 00:39 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Keith Thompson <kst-u@mib.org> - 2011-11-22 13:18 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Nick Keighley <nick_keighley_nospam@hotmail.com> - 2011-11-24 01:50 -0800
Re: Euler's constant jacob navia <jacob@spamsink.net> - 2011-11-21 12:45 +0100
Re: Euler's constant Vincenzo Mercuri <vincenzo.mercuri@yahoo.it> - 2011-11-21 13:54 +0100
Re: Euler's constant jacob navia <jacob@spamsink.net> - 2011-11-21 14:48 +0100
Re: Euler's constant Vincenzo Mercuri <vincenzo.mercuri@yahoo.it> - 2011-11-21 18:58 +0100
Re: Euler's constant Markus Wichmann <nullplan@gmx.net> - 2011-11-21 14:10 +0100
Re: Euler's constant jacob navia <jacob@spamsink.net> - 2011-11-21 15:36 +0100
Re: Euler's constant 88888 Dihedral <dihedral88888@googlemail.com> - 2011-11-21 07:08 -0800
Re: Euler's constant jacob navia <jacob@spamsink.net> - 2011-11-21 16:16 +0100
Re: Euler's constant Nick Keighley <nick_keighley_nospam@hotmail.com> - 2011-11-22 00:44 -0800
Re: Euler's constant Ben Bacarisse <ben.usenet@bsb.me.uk> - 2011-11-21 15:33 +0000
Re: Euler's constant Malcolm McLean <malcolm.mclean5@btinternet.com> - 2011-11-21 08:50 -0800
Re: Euler's constant "BartC" <bc@freeuk.com> - 2011-11-21 17:13 +0000
Re: Euler's constant James Kuyper <jameskuyper@verizon.net> - 2011-11-21 12:29 -0500
Re: Euler's constant Malcolm McLean <malcolm.mclean5@btinternet.com> - 2011-11-21 09:28 -0800
Re: Euler's constant Ben Bacarisse <ben.usenet@bsb.me.uk> - 2011-11-21 23:07 +0000
Re: Euler's constant Kaz Kylheku <kaz@kylheku.com> - 2011-11-21 17:29 +0000
Re: Euler's constant James Kuyper <jameskuyper@verizon.net> - 2011-11-21 12:36 -0500
Re: Euler's constant Keith Thompson <kst-u@mib.org> - 2011-11-21 13:46 -0800
Re: Euler's constant "io_x" <a@b.c.invalid> - 2011-11-24 19:08 +0100
Re: Euler's constant Markus Wichmann <nullplan@gmx.net> - 2011-11-24 20:31 +0100
Re: Euler's constant "io_x" <a@b.c.invalid> - 2011-11-27 11:24 +0100
Re: Euler's constant Markus Wichmann <nullplan@gmx.net> - 2011-11-27 12:09 +0100
Re: Euler's constant "io_x" <a@b.c.invalid> - 2011-11-27 13:33 +0100
Re: Euler's constant Lew Pitcher <lpitcher@teksavvy.com> - 2011-11-21 10:44 -0800
Re: Euler's constant Ben Bacarisse <ben.usenet@bsb.me.uk> - 2011-11-21 22:53 +0000
Re: Euler's constant Ben Bacarisse <ben.usenet@bsb.me.uk> - 2011-11-21 23:51 +0000
Re: Euler's constant 88888 Dihedral <dihedral88888@googlemail.com> - 2011-11-22 04:17 -0800
Re: Euler's constant 88888 Dihedral <dihedral88888@googlemail.com> - 2011-12-27 17:50 -0800
Re: Euler's constant Ben Bacarisse <ben.usenet@bsb.me.uk> - 2011-12-28 03:09 +0000
Re: Euler's constant 88888 Dihedral <dihedral88888@googlemail.com> - 2011-12-28 02:52 -0800
Re: Euler's constant Seebs <usenet-nospam@seebs.net> - 2011-12-28 18:17 +0000
Re: Euler's constant Dr Nick <3-nospam@temporary-address.org.uk> - 2011-12-28 18:49 +0000
Re: Euler's constant 88888 Dihedral <dihedral88888@googlemail.com> - 2012-01-04 04:44 -0800
Re: Euler's constant Robert Wessel <robertwessel2@yahoo.com> - 2012-01-04 12:33 -0600
Re: Euler's constant 88888 Dihedral <dihedral88888@googlemail.com> - 2011-11-21 15:07 -0800
Re: Euler's constant "io_x" <a@b.c.invalid> - 2011-11-24 19:08 +0100
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! 88888 Dihedral <dihedral88888@googlemail.com> - 2011-11-21 04:00 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Kleuskes & Moos <kleuske@somewhere.else.net> - 2011-11-21 12:37 +0000
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! 88888 Dihedral <dihedral88888@googlemail.com> - 2011-11-21 04:45 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Kleuskes & Moos <kleuske@somewhere.else.net> - 2011-11-21 13:35 +0000
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Phil Carmody <thefatphil_demunged@yahoo.co.uk> - 2011-11-22 00:01 +0200
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Kleuskes & Moos <kleuske@somewhere.else.net> - 2011-11-22 11:53 +0000
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Keith Thompson <kst-u@mib.org> - 2011-11-22 13:21 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Kleuske <kleuske@nowhere.net> - 2011-11-24 14:50 +0000
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! "io_x" <a@b.c.invalid> - 2011-11-24 14:08 +0100
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! "io_x" <a@b.c.invalid> - 2011-11-24 18:02 +0100
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Lew Pitcher <lpitcher@teksavvy.com> - 2011-11-25 15:31 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! 88888 Dihedral <dihedral88888@googlemail.com> - 2011-11-25 17:40 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Lew Pitcher <lpitcher@teksavvy.com> - 2011-11-25 22:03 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! 88888 Dihedral <dihedral88888@googlemail.com> - 2011-11-25 22:43 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Joe Wright <joewwright@comcast.net> - 2011-11-26 02:13 -0500
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! 88888 Dihedral <dihedral88888@googlemail.com> - 2011-11-26 19:40 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! 88888 Dihedral <dihedral88888@googlemail.com> - 2011-11-27 15:35 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Ian Collins <ian-news@hotmail.com> - 2011-11-26 20:22 +1300
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Lew Pitcher <lpitcher@teksavvy.com> - 2011-11-26 10:55 -0500
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Seebs <usenet-nospam@seebs.net> - 2011-11-28 08:32 +0000
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! superpollo <superpollo@tznvy.pbz> - 2011-11-26 12:11 +0100
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Lew Pitcher <lpitcher@teksavvy.com> - 2011-11-26 10:37 -0500
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! superpollo <superpollo@tznvy.pbz> - 2011-11-26 21:48 +0100
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Keith Thompson <kst-u@mib.org> - 2011-11-28 01:56 -0800
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Lew Pitcher <lpitcher@teksavvy.com> - 2011-11-28 13:34 -0500
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! James Kuyper <jameskuyper@verizon.net> - 2011-11-28 13:45 -0500
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Lew Pitcher <lpitcher@teksavvy.com> - 2011-11-28 13:50 -0500
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! James Kuyper <jameskuyper@verizon.net> - 2011-11-28 14:32 -0500
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Kleuske <kleuske@nowhere.net> - 2011-11-28 21:16 +0000
Re: OK. LETS START REAL PROGRAMMING IN C FOR PROBLEMS!!! Keith Thompson <kst-u@mib.org> - 2011-11-28 14:59 -0800
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