default(realprecision,38);
check(a,b)=my(c=abs(a-b)); if(!c,oo, ceil(log(c)/log(10)));
f(s,x)=check(zetahurwitz(s,x)+zetahurwitz(s,x+1/2), 2^s*zetahurwitz(s,2*x));
f(Pi,Pi)
check(zetahurwitz(Pi,1),zeta(Pi))
check(zetahurwitz(1,Pi), -psi(Pi))
s = Pi+I*log(2);
check(zetahurwitz(s,1), zeta(s))
