论文标题
Ramanujan身份的转折
A Twist of a Ramanujan Identity
论文作者
论文摘要
Ramanujan写下以下身份\ begin {align*} \ sqrt {2 \ left（1 - \ frac {1} {3^2} {3^2} \ right）\ left（1 - \ frac {1} {1} {7^2} {7^2} {7^2} \ right（ \ frac {1} {19^2} \ right）}} \ = \ \ left（1 + \ frac {1} {7} \ right）\ left（1 + \ frac {1} {1} {11}} \ right）\ left（1 + \ frac {1} {1} {19} {19} \ right），\ end eend {align*atne op the this this opernity opernity ot this thise supplate supplate supplate supplate supplate supplate supplate opers opert opert operty？丽贝克提供了产生许多相似身份的公式，并认为好奇的身份与Landau-Ramanujan常数的倒数有关。在先前的工作中，Chu检查了身份中整数的必要条件，并证明只有许多这样的身份。在此注释中，我们将身份扭曲以使其具有无限的Ramanujan型身份。
Ramanujan wrote the following identity \begin{align*} \sqrt{2 \left(1 - \frac{1}{3^2}\right) \left(1 - \frac{1}{7^2}\right) \left(1 - \frac{1}{11^2}\right) \left(1 - \frac{1}{19^2}\right)} \ = \ \left(1 + \frac{1}{7}\right) \left(1 + \frac{1}{11}\right) \left(1 + \frac{1}{19}\right), \end{align*} on which Berndt asked "Is this an isolated result, or are there other identities of this type?". Rebák provided formulas that generate many similar identities and believed that the curious identity is related to the reciprocal of the Landau-Ramanujan constant. In a previous work, Chu examined necessary and sufficient conditions for the integers in the identity and proved that there are only finitely many such identities. In this note, we twist the identity to have infinitely many Ramanujan-type identities.
