Difference between revisions of "Jacobi theta 3"

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(Created page with "Let $q \in \mathbb{C}$ with $|q|<1$. The Jacobi $\vartheta_3$ function is defined by $$\vartheta_3(z,q)=1+2\displaystyle\sum_{k=1}^{\infty} q^{k^2} \cos(2kz),$$ where $\cos$ d...")
 
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=Properties=
 
=Properties=
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[[Squares of theta relation for Jacobi theta 1 and Jacobi theta 4]]<br />
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[[Squares of theta relation for Jacobi theta 2 and Jacobi theta 4]]<br />
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[[Squares of theta relation for Jacobi theta 3 and Jacobi theta 4]]<br />
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[[Squares of theta relation for Jacobi theta 4 and Jacobi theta 4]]<br />
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[[Sum of fourth powers of Jacobi theta 2 and Jacobi theta 4 equals fourth power of Jacobi theta 3]]<br />
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[[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 $\vartheta_3$ function is defined by $$\vartheta_3(z,q)=1+2\displaystyle\sum_{k=1}^{\infty} q^{k^2} \cos(2kz),$$ 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