# partialsum1(y,k,0,n) is partial sum of y index k from 1 to n ;


partialsum1(y_,k_,a_,b_):= sum(y,k,a,b);
partialsum1(y_,k_,b_):= sum(y,k,1,b);
partialsum1(y_,k_):= sum(y,k,1,n);

partialsum1(a_+b_,k_):= partialsum1(a,k)+partialsum1(b,k);

partialsum1(y_):=sum(y,k,1,n);