/usr/share/calc/zeta2.cal is in apcalc-common 2.12.5.0-1build1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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* zeta2 - Hurwitz Zeta function
*
* Calc is open software; you can redistribute it and/or modify it under
* the terms of the version 2.1 of the GNU Lesser General Public License
* as published by the Free Software Foundation.
*
* Calc is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
* Public License for more details.
*
* A copy of version 2.1 of the GNU Lesser General Public License is
* distributed with calc under the filename COPYING-LGPL. You should have
* received a copy with calc; if not, write to Free Software Foundation, Inc.
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*
* @(#) $Revision: 30.4 $
* @(#) $Id: zeta2.cal,v 30.4 2013/08/18 20:01:53 chongo Exp $
* @(#) $Source: /usr/local/src/bin/calc/cal/RCS/zeta2.cal,v $
*
* Under source code control: 2013/08/11 01:31:28
* File existed as early as: 2013
*/
/*
* hide internal function from resource debugging
*/
static resource_debug_level;
resource_debug_level = config("resource_debug", 0);
define hurwitzzeta(s,a){
local realpart_a imagpart_s tmp tmp1 tmp2 tmp3;
local sum1 sum2 sum3 i k n precision result limit;
local limit_function offset offset_squared rest_sum eps;
/*
According to Linas Vepstas' "An efficient algorithm for accelerating
the convergence of oscillatory series, useful for computing the
polylogarithm and Hurwitz zeta functions" the Euler-Maclaurin series
is the fastest in most cases.
With a lot of help of the PARI/GP implementation by Prof. Henri Cohen,
hence the different license.
*/
eps=epsilon( epsilon() * 1e-3);
realpart_a=re(a);
if(realpart_a>1.5){
tmp=floor(realpart_a-0.5);
sum1 = 0;
for( i = 1 ; i <= tmp ; i++){
sum1 += ( a - i )^( -s );
}
epsilon(eps);
return (hurwitzzeta(s,a-tmp)-sum1);
}
if(realpart_a<=0){
tmp=ceil(-realpart_a+0.5);
for( i = 0 ; i <= tmp-1 ; i++){
sum2 += ( a + i )^( -s );
}
epsilon(eps);
return (hurwitzzeta(s,a+tmp)+sum2);
}
precision=digits(1/epsilon());
realpart_a=re(s);
imagpart_s=im(s);
epsilon(1e-9);
result=s-1.;
if(abs(result)<0.1){
result=-1;
}
else
result=ln(result);
limit=(precision*ln(10)-re((s-.5)*result)+(1.*realpart_a)*ln(2.*pi()))/2;
limit=max(2,ceil(max(limit,abs(s*1.)/2)));
limit_function=ceil(sqrt((limit+realpart_a/2-.25)^2+(imagpart_s*1.)^2/4)/
pi());
if (config("user_debug") > 0) {
print "limit_function = " limit_function;
print "limit = " limit;
print "prec = " precision;
}
/* Full precison plus 5 digits angstzuschlag*/
epsilon( (10^(-precision)) * 1e-5);
tmp3=(a+limit_function+0.)^(-s);
sum3 = tmp3/2;
for(n=0;n<=limit_function-1;n++){
sum3 += (a+n)^(-s);
}
result=sum3;
offset=a+limit_function;
offset_squared=1./(offset*offset);
tmp1=2*s-1;
tmp2=s*(s-1);
rest_sum=bernoulli(2*limit);
for(k=2*limit-2;k>=2;k-=2){
rest_sum=bernoulli(k)+offset_squared*
(k*k+tmp1*k+tmp2)*rest_sum/((k+1)*(k+2));
}
rest_sum=offset*(1+offset_squared*tmp2*rest_sum/2);
result+=rest_sum*tmp3/(s-1);
epsilon(eps);
return result;
}
/*
* restore internal function from resource debugging
* report important interface functions
*/
config("resource_debug", resource_debug_level),;
if (config("resource_debug") & 3) {
print "hurwitzzeta(s,a)";
}
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