Difference between revisions of "Jacobi theta 1"
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[[Sum of fourth powers of Jacobi theta 2 and Jacobi theta 4 equals fourth power of Jacobi theta 3]]<br /> | [[Sum of fourth powers of Jacobi theta 2 and Jacobi theta 4 equals fourth power of Jacobi theta 3]]<br /> | ||
[[Derivative of Jacobi theta 1 at 0]]<br /> | [[Derivative of Jacobi theta 1 at 0]]<br /> | ||
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| + | =See also= | ||
| + | [[Jacobi theta 2]]<br /> | ||
| + | [[Jacobi theta 3]]<br /> | ||
| + | [[Jacobi theta 4]]<br /> | ||
=References= | =References= | ||
Revision as of 22:07, 25 June 2016
Let $q \in \mathbb{C}$ with $|q|<1$. The Jacobi $\vartheta_1$ function is defined by $$\vartheta_1(z,q)=2q^{\frac{1}{4}} \displaystyle\sum_{k=0}^{\infty} (-1)^k q^{k(k+1)} \sin(2k+1)z,$$ where $\sin$ denotes the sine function.
Properties
Squares of theta relation for Jacobi theta 1 and Jacobi theta 4
Squares of theta relation for Jacobi theta 2 and Jacobi theta 4
Squares of theta relation for Jacobi theta 3 and Jacobi theta 4
Sum of fourth powers of Jacobi theta 2 and Jacobi theta 4 equals fourth power of Jacobi theta 3
Derivative of Jacobi theta 1 at 0
See also
Jacobi theta 2
Jacobi theta 3
Jacobi theta 4
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 16.27.1
