{Sum[ClebschGordan[{l,m-m2},{s,m2},{j,m}]^2 m2,{m2,-s,s,1}],m(j(j+1)-l(l+1)+s(s+1))/(2j(j+1))} /. {j->l+1/2,s->1/2}
Simplify[%,Element[{l,m},Integers]]
            m        m
Out[2]= {-------, -------}
         1 + 2 l  1 + 2 l

{Sum[ClebschGordan[{l,m-m2},{s,m2},{j,m}]^2 m2,{m2,-s,s,1}],m(j(j+1)-l(l+1)+s(s+1))/(2j(j+1))} /. {j->l-1/2,s->1/2}
Simplify[%]
              m           m
Out[4]= {-(-------), -(-------)}
           1 + 2 l     1 + 2 l

{Sum[ClebschGordan[{l,m-m2},{s,m2},{j,m}]^2 m2,{m2,-s,s,1}],m(j(j+1)-l(l+1)+s(s+1))/(2j(j+1))} /. {j->l+1,s->1}
Simplify[%,Element[{l,m},Integers]]
           m      m
Out[6]= {-----, -----}
         1 + l  1 + l

{Sum[ClebschGordan[{l,m-m2},{s,m2},{j,m}]^2 m2,{m2,-s,s,1}],m(j(j+1)-l(l+1)+s(s+1))/(2j(j+1))} /. {j->l,s->1}
Simplify[%,Element[{l,m},Integers]]
           m       m
Out[8]= {------, ------}
              2       2
         l + l   l + l

{Sum[ClebschGordan[{l,m-m2},{s,m2},{j,m}]^2 m2,{m2,-s,s,1}],m(j(j+1)-l(l+1)+s(s+1))/(2j(j+1))} /. {j->l-1,s->1}
Simplify[%]
            m     m
Out[10]= {-(-), -(-)}
            l     l

{Sum[ClebschGordan[{l,m-m2 },{s,m2},{j,m}]^2 m2,{m2,-s,s,1}],m(j(j+1)-l(l+1)+s(s+1))/(2j(j+1))} /. {j->l+3/2,s->3/2}
Simplify[%,Element[{l,m},Integers]]
            3 m      3 m
Out[12]= {-------, -------}
          3 + 2 l  3 + 2 l

{Sum[ClebschGordan[{l,m-m2 },{s,m2},{j,m}]^2 m2,{m2,-s,s,1}],m(j(j+1)-l(l+1)+s(s+1))/(2j(j+1))} /. {j->l+1/2,s->3/2}
Simplify[%,Element[{l,m},Integers]]
           (9 + 2 l) m     (9 + 2 l) m
Out[14]= {--------------, --------------}
                       2               2
          3 + 8 l + 4 l   3 + 8 l + 4 l

{Sum[ClebschGordan[{l,m-m2 },{s,m2},{j,m}]^2 m2,{m2,-s,s,1}],m(j(j+1)-l(l+1)+s(s+1))/(2j(j+1))} /. {j->l-1/2,s->3/2}
Simplify[%,Element[{l,m},Integers]]
          (7 - 2 l) m  (7 - 2 l) m
Out[16]= {-----------, -----------}
                   2            2
           -1 + 4 l     -1 + 4 l

{Sum[ClebschGordan[{l,m-m2 },{s,m2},{j,m}]^2 m2,{m2,-s,s,1}],m(j(j+1)-l(l+1)+s(s+1))/(2j(j+1))} /. {j->l-3/2,s->3/2}
Simplify[%]
            3 m      3 m
Out[18]= {-------, -------}
          1 - 2 l  1 - 2 l

{Sum[ClebschGordan[{l,m-m2 },{s,m2},{j,m}]^2 m2,{m2,-s,s,1}],m(j(j+1)-l(l+1)+s(s+1))/(2j(j+1))} /. {j->l+2,s->2}
Simplify[%,Element[{l,m},Integers]]
           2 m    2 m
Out[20]= {-----, -----}
          2 + l  2 + l

{Sum[ClebschGordan[{l,m-m2 },{s,m2},{j,m}]^2 m2,{m2,-s,s,1}],m(j(j+1)-l(l+1)+s(s+1))/(2j(j+1))} /. {j->l+1,s->2}
Simplify[%,Element[{l,m},Integers]]
           (4 + l) m     (4 + l) m
Out[22]= {------------, ------------}
                     2             2
          2 + 3 l + l   2 + 3 l + l

{Sum[ClebschGordan[{l,m-m2 },{s,m2},{j,m}]^2 m2,{m2,-s,s,1}],m(j(j+1)-l(l+1)+s(s+1))/(2j(j+1))} /. {j->l,s->2}
Simplify[%,Element[{l,m},Integers]]
           3 m     3 m
Out[24]= {------, ------}
               2       2
          l + l   l + l

{Sum[ClebschGordan[{l,m-m2 },{s,m2},{j,m}]^2 m2,{m2,-s,s,1}],m(j(j+1)-l(l+1)+s(s+1))/(2j(j+1))} /. {j->l-1,s->2}
Simplify[%,Element[{l,m},Integers]]
            (-3 + l) m     (-3 + l) m
Out[26]= {-(----------), -(----------)}
            (-1 + l) l     (-1 + l) l

{Sum[ClebschGordan[{l,m-m2 },{s,m2},{j,m}]^2 m2,{m2,-s,s,1}],m(j(j+1)-l(l+1)+s(s+1))/(2j(j+1))} /. {j->l-2,s->2}
Simplify[%]
           -2 m    -2 m
Out[28]= {------, ------}
          -1 + l  -1 + l

