On the 2- and 4-dissections of Ramanujan’s continued fraction and its reciprocal
On the 2- and 4-dissections of Ramanujan’s continued fraction and its reciprocal
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DOI：
10.1007/s11139-010-9272-z
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
M. Hirschhorn
中科院分区：
文献类型：
--
作者：
M. Hirschhorn
我们仅用Jacobi的三重积恒等式，给出了Ramanujan的四个恒等式和Hirschhorn的八个恒等式的初等证明，这些恒等式与Ramanujan的连分式及其倒数的2-剖析和4-剖析有关，以及Ramanujan著名的40个恒等式中的两个恒等式。
We present elementary proofs, using only Jacobi’s triple product identity, of four identities of Ramanujan and eight identities of Hirschhorn relating to the 2-dissection and the 4-dissection of Ramanujan’s continued fraction and its reciprocal, and of two identities from Ramanujan’s famous list of forty.