Difference between revisions of "Squares of theta relation for Jacobi theta 4 and Jacobi theta 4"
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(Created page with "==Theorem== The following formula holds: $$\vartheta_4^2(z,q)\vartheta_4^2(0,q)=\vartheta_3^2(z,q)\vartheta_3^2(0,q)-\vartheta_2^2(z,q)\vartheta_2^2(0,q),$$ where $\vartheta_4...") |
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==References== | ==References== | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Squares of theta relation for Jacobi theta 3 and Jacobi theta 4|next=Sum of fourth powers of Jacobi theta 2 and Jacobi theta 4 equals fourth power of Jacobi theta 3}}: 16.28.4 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Squares of theta relation for Jacobi theta 3 and Jacobi theta 4|next=Sum of fourth powers of Jacobi theta 2 and Jacobi theta 4 equals fourth power of Jacobi theta 3}}: $16.28.4$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Latest revision as of 18:04, 5 July 2016
Theorem
The following formula holds: $$\vartheta_4^2(z,q)\vartheta_4^2(0,q)=\vartheta_3^2(z,q)\vartheta_3^2(0,q)-\vartheta_2^2(z,q)\vartheta_2^2(0,q),$$ where $\vartheta_4$ denotes the Jacobi theta 4, $\vartheta_3$ denotes the Jacobi theta 3, and $\vartheta_2$ denotes Jacobi theta 2.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $16.28.4$
