We give simple proofs of Hecke–Rogers indefinite binary theta series identities for the two Ramanujan’s fifth order mock theta functions \(\chi _0(q)\) and \(\chi _1(q)\) and all three of Ramanujan’s seventh order mock theta functions. We find that the coefficients of the three mock theta functions of order 7 are surprisingly related.

中文翻译：

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新的五阶和七阶模拟Theta函数身份

我们给出了两个拉曼努詹的五阶模拟theta函数\（\ chi _0（q）\）和\（\ chi _1（q）\）以及三个拉曼努詹第七阶的Hecke-Rogers不定二进制theta系列恒等式的简单证明模拟theta函数。我们发现，阶数为7的三个模拟theta函数的系数令人惊讶地相关。