Written by Yasuaki dot Honda at gmail dot com
Copyright 2020 Yasuaki Honda
GPL2.0
Application to Euler Mascheroni constant is taken from the following PDF:
http://people.csail.mit.edu/kuat/courses/euler-maclaurin.pdf
install_github("YasuakiHonda","euler-maclaurin-sum","master");
asdf_load_source("euler-maclaurin-sum");
ems;
assume(M>1);
ems,f(x):=1/x,N:1,K:1;
%,nouns;
EuGamma:%-log(M);
plot2d([bernpoly(x-floor(x),1),bernpoly(x-floor(x),1)/x^2,1/x^2],[x,1,5])$
apply1(first(rhs(EuGamma)), emsRemInt);
rem:%,M:100,nouns,numer;
limit(rest(rhs(EuGamma)),M,inf)+rem,numer;
%gamma,numer;
assume(M-10000>0);
ems,f(x):=1/x,N:10000,K:6,nouns;
EuGamma:%-log(M);
diff(bernpoly(x,6),x),factor;
[bernpoly(0,6),bernpoly(1/2,6),bernpoly(1,6)];
[err:integrate(%[1]/x^7,x,10000,inf),ev(err,numer)];
fpprec:30;
bfloat(sum(1/n,n,1,9999)+limit(rest(rhs(EuGamma)),M,inf));
bfloat(%gamma);