# harmonic(n) is Harmonic number =sum(1/k,k,1,n); # harmonic(a,x) is genelized Harmonic number function =sum(1/k^a,k,1,x); # harmonic(a,1,x) is incomplete genelized harmonic number =integrate((1-t^a)/(1-t),t,0,x) ; harmonic(a_,b_,0):=0; harmonic(a_,b_,1):=harmonic(a,b); harmonic(a_,b_,inf):=zeta(a,b); harmonic(-5,n_) := (-1/12)*n^2+5/12*n^4+1/2*n^5+1/6*n^6; harmonic(-4,n_) := (-1/30)*n+1/3*n^3+1/2*n^4+1/5*n^5; harmonic(-3,x_):= x^4/4+x^3/2+x^2/4; harmonic(-2,x_):= x^3/3+x^2/2+x/6; harmonic(-1,n_):= (n^2+n)/2; harmonic(0,n_):=n; harmonic(1,n_):=harmonic(n); harmonic(a_,0):=0; harmonic(a_,1):=1; harmonic(a_,inf):=zeta(a); harmonic(1):=1; harmonic(inf):=inf;