Difference between revisions of "Derivative of Jacobi theta 1 at 0"

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(Created page with "==Theorem== The following formula holds: $$\vartheta_1'(0,q)=\vartheta_2(0,q) \vartheta_3(0,q) \vartheta_4(0,q),$$ where $\vartheta_1$ denotes the Jacobi theta 1, $\varthe...")
 
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==References==
 
==References==
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Sum of fourth powers of Jacobi theta 2 and Jacobi theta 4 equals fourth power of Jacobi theta 3|next=findme}}: 16.28.6
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* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Sum of fourth powers of Jacobi theta 2 and Jacobi theta 4 equals fourth power of Jacobi theta 3|next=Logarithmic derivative of Jacobi theta 1 equals cotangent + a sum of sines}}: 16.28.6
  
 
[[Category:Theorem]]
 
[[Category:Theorem]]
 
[[Category:Unproven]]
 
[[Category:Unproven]]

Revision as of 07:10, 27 June 2016

Theorem

The following formula holds: $$\vartheta_1'(0,q)=\vartheta_2(0,q) \vartheta_3(0,q) \vartheta_4(0,q),$$ where $\vartheta_1$ denotes the Jacobi theta 1, $\vartheta_2$ denotes the Jacobi theta 2, $\vartheta_3$ denotes Jacobi theta 3, and $\vartheta_4$ denotes Jacobi theta 4.

Proof

References