Ramanujan立体和连分数倒数的2-剖分的证明

A proof on 2-dissection of Ramanujan cubic continued fraction reciprocal

2010年,Hirschhorn和Roselin给出了Ramanujan立体和连分数及其倒数的2-剖分,用不同的方法证明Ramanujan立体和连分数倒数的2-剖分,并利用相关的幂级数恒等式证明这两个表达式等价.

In 2010,Hirschhorn and Roselin gave 2-dissection of Ramanujan’s cubic continuous fractions and their reciprocal.In this paper,we prove the 2-dissection of Ramanujan’s cubic continuous fraction reciprocal in a different way,and then further prove the equivalence of these two expressions by using related power series identities.