Difference between revisions of "Jacobi theta 4"
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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 /> | ||
| + | [[Logarithm of a quotient of Jacobi theta 4 equals a sum of sines]]<br /> | ||
=See also= | =See also= | ||
Revision as of 16:39, 27 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
Logarithm of a quotient of Jacobi theta 4 equals a sum of sines
See also
Jacobi theta 1
Jacobi theta 2
Jacobi theta 3
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 16.27.4
