# infsum1() is infinite sum y with index k from 1 to inf;

infsum1(y_,k_):=sum(y,k,1,inf);
infsum1(y_+z_,k_):=sum(y,k,1,inf)+sum(z,k,1,inf);
infsum1(y_):=sum(y,k,1,inf);
infsum1(y_+z_):=sum(y,k,1,inf)+sum(z,k,1,inf);
infsum1(c_*(y_+z_)):=sum(y*c,k,1,inf)+sum(z*c,k,1,inf);