# beta(s) is Dirichlet beta function of integral from 0 to inf; # beta(s,x) is incomplete Dirichlet beta function of integral from x to oo; # beta(s,0,x) is incomplete Dirichlet beta function of integral from 0 to x; # beta(s,a,x) is incomplete Dirichlet beta function of integral from a to x; #beta(s_,a_,b_):=beta(s,a)-beta(s,b); beta(s_,a_,a_) :=0; beta(s_,0,b_):=beta(s)-beta(s,b); beta(s_,0,inf) := beta(s); beta(s_,0) :=beta(s); beta(s_,oo) :=0; beta(0):=1/2; beta(1):=pi/4;