Difference between revisions of "Jacobi theta 2"
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| − | The Jacobi $\vartheta_2$ function is defined by | + | Let $q \in \mathbb{C}$ with $|q|<1$. The Jacobi $\vartheta_2$ function is defined by |
$$\vartheta_2(z,q)=2q^{\frac{1}{4}}\displaystyle\sum_{k=0}^{\infty} q^{k(k+1)} \cos(2k+1)z,$$ | $$\vartheta_2(z,q)=2q^{\frac{1}{4}}\displaystyle\sum_{k=0}^{\infty} q^{k(k+1)} \cos(2k+1)z,$$ | ||
where $\cos$ denotes the [[cosine]] function. | where $\cos$ denotes the [[cosine]] function. | ||
Revision as of 21:37, 25 June 2016
Let $q \in \mathbb{C}$ with $|q|<1$. The Jacobi $\vartheta_2$ function is defined by $$\vartheta_2(z,q)=2q^{\frac{1}{4}}\displaystyle\sum_{k=0}^{\infty} q^{k(k+1)} \cos(2k+1)z,$$ where $\cos$ denotes the cosine function.
Properties
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 16.27.2
