Difference between revisions of "Jacobi theta 3"

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=References=
 
=References=
 
* {{BookReference|Special Functions|1960|Earl David Rainville|prev=Jacobi theta 2|next=Jacobi theta 4}}: $164. (3)$
 
* {{BookReference|Special Functions|1960|Earl David Rainville|prev=Jacobi theta 2|next=Jacobi theta 4}}: $164. (3)$
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Jacobi theta 2|next=Jacobi theta 4}}: 16.27.3
+
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Jacobi theta 2|next=Jacobi theta 4}}: $16.27.3$
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Revision as of 18:03, 5 July 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
Logarithm of quotient of Jacobi theta 3 equals a sum of sines

See also

Jacobi theta 1
Jacobi theta 2
Jacobi theta 4

References