On the paper “A ‘lost’ notebook of Ramanujan”
On the paper “A ‘lost’ notebook of Ramanujan”
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DOI：
10.1016/0001-8708(84)90027-6
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发表时间：
1984-09
影响因子：
1.7
通讯作者：
R. Agarwal
中科院分区：
文献类型：
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作者：
R. Agarwal
在一系列的两个最近的文件安德鲁斯[2，31]讨论了介绍拉马努金的“失去”笔记本（因为他已经称之为），并讨论了详细，某些群体的公式中发现的笔记本。在第二次的两份文件安德鲁斯'了几个显着的和天真的证明一些拉马努金的棘手和神秘的身份。他还在他的论文中提出了一些应用这些身份分区。安德鲁斯的辉煌工作提供了一个新的推动力，研究与解开的奥秘背后拉马努金的工作。一个主要的结果，安德鲁斯已得出在[3]是在他的定理我（3.1），他呼吁作为“关键”的结果，以证明许多拉马努金的身份为“部分”θ函数。在他的论文的结论中，安德鲁斯[3]评论说：“将基本定理I放在基本超几何级数恒等式文献中的适当位置将是特别好的。这样的成就无疑会导致更好的解释和进一步扩展的部分θ函数。
In a series of two recent papers Andrews [2, 31 has discussed an introduction to Ramanujan’s “lost” notebook (as he has called it) and has discussed, in detail, certain groups of formulae found in that notebook. In the second of the two papers Andrews’ has given several remarkable and ingeneous proofs for some of the Ramanujan’s tricky and mysterious identities. He has also given in his paper the application of some of these identities to partitions. The splendid work of Andrews has given a fresh impetus to research connected with unraveling the mysteries underlying Ramanujan’s work.One of the major results that Andrews has derived in [3] is given in his Theorem I (3.1) which he calls as the “key” result to proving many of Ramunajan’s identities for “partial” theta functions. In the concluding remarks of his paper Andrews [3] remarks that “it would be especially nice to place the fundamental Theorem I in an appropriate place in the literature of basic hypergeometric series identities. Such an achievement would undoubtedly lead to better explanation and further extension of partial theta functions.”