On The 2-Dissection And 3-Dissection Of Ramanujan-G(?)llnitz-Gordon’s Continued Fraction And Its Reciprocal

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 P_k =（?）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≠qⁿa_j for i≠j,n∈Z,a₁a₂…a_n=b₁b₂ … b_n）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.