theta-function

Furthermore, we introduce the notion of theta decompositions to derive new theta function identities. We explain how to transform the set of the theta function solutions of a given contiguous relation into a finite dimensional vector space over the field K ( q).

进一步，为了推导新的恒等式，我们引入了theta分解的概念，说明了给定邻接关系的theta函数解空间可以转化为域K（q）上的有限维向量空间。

The two-term contiguous relations satisfied by a given theta function can be obtained by straightforward calculations and the number of the initial values depends on the dimension of the theta function.

其中，theta函数满足的两项邻接关系可以直接计算得到，而初始系数个数的确定则有赖于theta函数的维数。

The new theta function identities can be derived by considering the linear dependence relations among the elements of the vector space.

通过研究向量之间的线性相关性即可得到新的theta函数恒等式。

Rogers-Ramanujan Type Identities and False Theta Function Formulae

Rogers-Ramanujan类型恒等式与部分theta函数公式

An Important Theta Function Identity and Its Applications

一个重要的Theta函数恒等式及其应用

Well, now that it's only a function of a and theta, I know what it means to take the partial derivative with respect to theta, keeping a constant. I know how to do it.

现在它成了一个只关于a和θ的函数，我知道保持a恒定不变，关于θ的偏导数是什么，我知道这怎么做。