A reciprocity theorem for certain q-series found in Ramanujan’s lost notebook
A reciprocity theorem for certain q-series found in Ramanujan’s lost notebook
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DOI：
10.1007/s11139-006-0241-5
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发表时间：
2007-06
期刊：
影响因子：
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通讯作者：
B. Berndt;Song Heng Chan;B. P. Yeap;A. Yee
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文献类型：
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作者：
B. Berndt;Song Heng Chan;B. P. Yeap;A. Yee
给出了拉马努金丢失的笔记本中发现的某个 q 级数的互易定理的三个证明。第一个证明使用拉马努金的 1ψ1 求和定理，第二个证明使用 N. J. Fine 恒等式，第三个证明是组合证明。接下来，我们证明互反定理导致五元乘积恒等式的二变量推广。本文最后给出了三个平方和的应用。
Three proofs are given for a reciprocity theorem for a certainq-series found in Ramanujan’s lost notebook. The first proof uses Ramanujan’s1ψ1summation theorem, the second employs an identity of N. J. Fine, and the third is combinatorial. Next, we show that the reciprocity theorem leads to a two variable generalization of the quintuple product identity. The paper concludes with an application to sums of three squares.