Difference between revisions of "Jacobi theta 4"
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| Line 4: | Line 4: | ||
=Properties= | =Properties= | ||
| + | [[Squares of theta relation for Jacobi theta 1 and Jacobi theta 4]]<br /> | ||
| + | [[Squares of theta relation for Jacobi theta 2 and Jacobi theta 4]]<br /> | ||
| + | [[Squares of theta relation for Jacobi theta 3 and Jacobi theta 4]]<br /> | ||
| + | [[Squares of theta relation for Jacobi theta 4 and Jacobi theta 4]]<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 /> | ||
=References= | =References= | ||
Revision as of 22:00, 25 June 2016
Let $q \in \mathbb{C}$ with $|q|<1$. The Jacobi $\vartheta_4$ function is defined by $$\vartheta_4(z,q)=1+2\displaystyle\sum_{k=1}^{\infty} (-1)^k q^{k^2} \cos(2kz),$$ where $\cos$ denotes the cosine 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
Squares of theta relation for Jacobi theta 4 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
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 16.27.4
