.nf
.EQ
G(z)~=~ e sup { ln~G(z) }
~=~ exp left (
        sum from k>=1 {S sub k z sup k} over k
        right )
~=~ prod from k>=1 e sup { S sub k z sup k /k }
.EN
.sp
.EQ
~~~~~~~= left (
        1 + S sub 1 z
        + { S sub 1 sup 2 z sup 2 } over 2!
        + ...
        right )
        left (
        1 + { S sub 2 z sup 2 } over 2
        + { S sub 2 sup 2 z sup 4 } over { 2 sup 2 cdot 2! }
        + ...
        right )
        ...
.EN
.sp
.EQ
~~~~~~~= sum from m>=0
        left (
                sum from
                        pile { k sub 1 , k sub 2 , ... , k sub m >= 0
                        above  k sub 1 +2k sub 2 + ... +mk sub m = m }
                { S sub 1 sup { k sub 1 } } over { 1 sup k sub 1 k sub 1 ! } ~
                { S sub 2 sup { k sub 2 } } over { 2 sup k sub 2 k sub 2 ! } ~
                ...
                { S sub m sup { k sub m } } over { m sup k sub m k sub m ! } ~
        right )
        z sup m
.EN
.pl \n(nl
