The Ramanujan's lost notebook is an important mathematical achievement of S.Ramanujan,a famous mathematician in India.Ramanujan continued fraction is one of the contents in the Ramanujan's lost notebook,and the Ramanujan-G???llnitz-Gordon?or called Gordon continued fraction?is a special type of Ramanujan con-tinued fraction,which is defined as follows:If the power series P =???anqn can be expressed as P = P0 + P1 +...+Pm-1,where Pk =???amn+kqmn+k,it is called the m-dissection of power series P.Hirschhorn proved the 2-dissection and 3-dissection of Gordon continued fraction G?q?and it's reciprocal G?q?-1 by the Jacobi triple product identity.In the present paper,by using the following identity?where ai?qnaj for i?j,n?Z,a1a2…an=b1b2 … bn?we have given a different method to prove the 2-dissection and 3-dissection of Gordon continued fraction and it,s reciprocal from different angles. |