Question: coefficient of polynom

> f:=(1./x)*ln((1.+x)/(1-x));
                                 /1. + x\
                            1. ln|------|
                                 \1 - x /
                       f := -------------
                                  x     

> L:=sum(p[i]*x^i,i=0..3);
                                        2         3
             L := p[0] + p[1] x + p[2] x  + p[3] x
> M:=1+sum(q[i]*x^i,i=1..2);
                                           2
                   M := 1 + q[1] x + q[2] x
> T:=convert(taylor(f*M-L,x=0,3),polynom);
  T := 2.000000000 - 1. p[0] + (2.000000000 q[1] - 1. p[1]) x
> T1:=convert(series(f*M-L,x=infinity,5),polynom);
                3            2                                             
T1 := -1. p[3] x  - 1. p[2] x  + (-1. p[1] + 3.141592654 I q[2]) x - 1. p[0]

                                    3.141592654 I + 2. q[1]
   + 3.141592654 I q[1] + 2. q[2] + -----------------------
                                               x          

     2. + 0.6666666667 q[2]   0.6666666667 q[1]
   + ---------------------- + -----------------
                2                     3       
               x                     x        
> eqs:={seq(coeftayl(T,x=0,j),j=0..3)}union{seq(coeff(T1,x=infinity,j),j=1..4)};
 eqs := {0, 2.000000000 - 1. p[0], 2.000000000 q[1] - 1. p[1]}

here i want to collect all the coefficient of T and T it is good with T but I don't know what to do with T1

can you give me why?

thanks