# Phi(x,s,a) is Lerch() function ;
# =sum(x^k/(a+k)^s,k,0,inf) ;
# =integrate(t^(s-1)*exp(-a*t+t)/(exp(t)-x),t,0,inf)/gamma(s);


Phi(x_,s_,1):=polylog(s,x)/x;
Phi(1,s_,c_):=zeta(s,c);
Phi(-1,x_,c_):=eta(x,c);
Phi(a_,b_,0):=Phi(a,b);
Phi(a_,b_,inf):=0;

Phi(a_,b_,c_,inf):=Phi(a,b,c);
Phi(a_,b_,c_, -inf):= -Phi(a,b,c);
Phi(a_,b_,c_,0):=0;

Phi(0):=1/2;
Phi(oo):=1;
Phi(-oo):=0;